Bulletin of the London Mathematical Society最新文献_第9页

Approximate identities for ideals in L ( L p ) $L(L^p)$ L(L p)$ L(L^p)$理想的近似恒等式

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-09-28 DOI: 10.1112/blms.13161

W. B. Johnson, G. Schechtman

{"title":"Approximate identities for ideals in \u0000 \u0000 \u0000 L\u0000 (\u0000 \u0000 L\u0000 p\u0000 \u0000 )\u0000 \u0000 $L(L^p)$","authors":"W. B. Johnson, G. Schechtman","doi":"10.1112/blms.13161","DOIUrl":"https://doi.org/10.1112/blms.13161","url":null,"abstract":"The main result is that the only non-trivial closed ideal in the Banach algebra <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$L(L^p)$</annotation>\u0000 </semantics></math> of bounded linear operators on <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L^p(0,1)$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>⩽</mo>\u0000 <mi>p</mi>\u0000 <mo><</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$1leqslant p < infty$</annotation>\u0000 </semantics></math>, that has a left approximate identity is the ideal of compact operators. The algebra <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$L(L^1)$</annotation>\u0000 </semantics></math> has at least one non-trivial closed ideal that has a contractive right approximate identity as well as many, including the unique maximal ideal, that do not have a right approximate identity.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 12","pages":"3708-3720"},"PeriodicalIF":0.8,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An analogue of the Mellin transform for weakly holomorphic cusp forms and a converse theorem 弱全纯尖形的Mellin变换的一个类似性质及一个逆定理

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-09-27 DOI: 10.1112/blms.13163

Ö. Imamoḡlu, Y. Martin, Á. Tóth

{"title":"An analogue of the Mellin transform for weakly holomorphic cusp forms and a converse theorem","authors":"Ö. Imamoḡlu, Y. Martin, Á. Tóth","doi":"10.1112/blms.13163","DOIUrl":"https://doi.org/10.1112/blms.13163","url":null,"abstract":"We define an analogue of the classical Mellin transform for vector-valued weakly holomorphic cusp forms for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>Z</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$SL(2,mathbb {Z})$</annotation>\u0000 </semantics></math> and prove a converse theorem for such forms in terms of the new transform. As applications we get converse theorems for scalar valued weakly holomorphic forms for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>Z</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$SL(2,mathbb {Z})$</annotation>\u0000 </semantics></math> as well as <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>Γ</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$Gamma _0(p)$</annotation>\u0000 </semantics></math> for primes <math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 12","pages":"3731-3744"},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Holomorphically conjugate polynomial automorphisms of C 2 $mathbb {C}^2$ are polynomially conjugate c2 $mathbb {C}^2$的全纯共轭多项式自同构是多项式共轭的

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-09-26 DOI: 10.1112/blms.13164

Serge Cantat, Romain Dujardin

{"title":"Holomorphically conjugate polynomial automorphisms of \u0000 \u0000 \u0000 C\u0000 2\u0000 \u0000 $mathbb {C}^2$\u0000 are polynomially conjugate","authors":"Serge Cantat, Romain Dujardin","doi":"10.1112/blms.13164","DOIUrl":"https://doi.org/10.1112/blms.13164","url":null,"abstract":"We confirm a conjecture of Friedland and Milnor: if two polynomial automorphisms <math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mo>∈</mo>\u0000 <mi>Aut</mi>\u0000 <mo>(</mo>\u0000 <msubsup>\u0000 <mi>A</mi>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msubsup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$gin mathsf {Aut}(mathbb {A}^2_mathbf {C})$</annotation>\u0000 </semantics></math> with dynamical degree greater than 1 are conjugate by some holomorphic diffeomorphism <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>φ</mi>\u0000 <mo>:</mo>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$varphi colon mathbf {C}^2rightarrow mathbf {C}^2$</annotation>\u0000 </semantics></math>, then <math>\u0000 <semantics>\u0000 <mi>φ</mi>\u0000 <annotation>$varphi$</annotation>\u0000 </semantics></math> is a polynomial automorphism; thus, <math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math> are conjugate inside <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Aut</mi>\u0000 <mo>(</mo>\u0000 <msubsup>\u0000 <mi>A</mi>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msubsup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathsf {Aut}(mathbb {A}^2_mathbf {C})$</annotation>\u0000 </semantics></math>. We also discuss a number of variations on this result.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 12","pages":"3745-3751"},"PeriodicalIF":0.8,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13164","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142851551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Curves are algebraic K ( π , 1 ) $K(pi,1)$ : Theoretical and practical aspects 曲线是代数K(π,1)$ K(pi,1)$：理论和实践两个方面

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-09-25 DOI: 10.1112/blms.13153

Christophe Levrat

{"title":"Curves are algebraic \u0000 \u0000 \u0000 K\u0000 (\u0000 π\u0000 ,\u0000 1\u0000 )\u0000 \u0000 $K(pi,1)$\u0000 : Theoretical and practical aspects","authors":"Christophe Levrat","doi":"10.1112/blms.13153","DOIUrl":"https://doi.org/10.1112/blms.13153","url":null,"abstract":"We prove that any geometrically connected curve <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> over a field <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math> is an algebraic <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <mo>(</mo>\u0000 <mi>π</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$K(pi,1)$</annotation>\u0000 </semantics></math>, as soon as its geometric irreducible components have nonzero genus. This means that the cohomology of any locally constant constructible étale sheaf of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Z</mi>\u0000 <mo>/</mo>\u0000 <mi>n</mi>\u0000 <mi>Z</mi>\u0000 </mrow>\u0000 <annotation>$mathbb {Z}/nmathbb {Z}$</annotation>\u0000 </semantics></math>-modules, with <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> invertible in <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>, is canonically isomorphic to the cohomology of its corresponding <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>π</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$pi _1(X)$</annotation>\u0000 </semantics></math>-module. To this end, we explicitly construct some Galois coverings of <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> corresponding to Galois coverings of the normalisation of its irreducible components. When <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math> is finite or algebraically closed, we precisely describe finite quotients of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>π</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$pi _1(X)$</annotation>\u0000 </semantics></math> that allow to compute the cohomology groups ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 12","pages":"3601-3622"},"PeriodicalIF":0.8,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type 非紧型黎曼对称空间间的调和黎曼淹没

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-09-25 DOI: 10.1112/blms.13155

F. E. Burstall

引用次数: 0

On the relation between pseudocharacters and Chenevier's determinants 论伪字符与切内维埃行列式之间的关系

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-09-25 DOI: 10.1112/blms.13162

Amit Ophir

{"title":"On the relation between pseudocharacters and Chenevier's determinants","authors":"Amit Ophir","doi":"10.1112/blms.13162","DOIUrl":"https://doi.org/10.1112/blms.13162","url":null,"abstract":"Consider a commutative unital ring <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> and a unital <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>-algebra <math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math>. Let <math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math> be a positive integer. Chenevier proved that when <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mi>d</mi>\u0000 <mo>)</mo>\u0000 <mo>!</mo>\u0000 </mrow>\u0000 <annotation>$(2d)!$</annotation>\u0000 </semantics></math> is invertible in <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>, the map associating to a determinant its trace is a bijection between <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>-valued <math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math>-dimensional determinants of <math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>-valued <math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math>-dimensional pseudocharacters of <math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math>. In this paper, we show that assuming <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>!</mo>\u0000 </mrow>\u0000 <annotation>$d!$</annotation>\u0000 </semantics></math> is invertible in <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> is sufficient. This assumption is already made in the definition of a <math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$<","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 12","pages":"3721-3730"},"PeriodicalIF":0.8,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13162","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Structure of the Kuranishi spaces of pairs of Kähler manifolds and polystable Higgs bundles 成对凯勒流形和多稳希格斯束的仓西空间结构

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-09-25 DOI: 10.1112/blms.13152

Takashi Ono

{"title":"Structure of the Kuranishi spaces of pairs of Kähler manifolds and polystable Higgs bundles","authors":"Takashi Ono","doi":"10.1112/blms.13152","DOIUrl":"https://doi.org/10.1112/blms.13152","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> be a compact Kähler manifold and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>E</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mover>\u0000 <mi>∂</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <mi>E</mi>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mi>θ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(E,overline{partial }_E,theta)$</annotation>\u0000 </semantics></math> be a Higgs bundle over it. We study the structure of the Kuranishi space for the pair <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mi>E</mi>\u0000 <mo>,</mo>\u0000 <mi>θ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(X, E,theta)$</annotation>\u0000 </semantics></math> when the Higgs bundle admits a harmonic metric or equivalently when the Higgs bundle is polystable and the Chern classes are 0. Under such assumptions, we show that the Kuranishi space of the pair <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mi>E</mi>\u0000 <mo>,</mo>\u0000 <mi>θ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(X,E,theta)$</annotation>\u0000 </semantics></math> is isomorphic to the direct product of the Kuranishi space of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>E</mi>\u0000 <mo>,</mo>\u0000 <mi>θ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(E,theta)$</annotation>\u0000 </semantics></math> and the Kuranishi space of <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>. Moreover, when <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> is a Riemann surface and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>E</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mover>\u0000 <mi>∂</","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 12","pages":"3581-3600"},"PeriodicalIF":0.8,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13152","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A note on a Halmos problem 关于Halmos问题的说明

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-09-24 DOI: 10.1112/blms.13159

Maximiliano Contino, Eva A. Gallardo-Gutiérrez

{"title":"A note on a Halmos problem","authors":"Maximiliano Contino, Eva A. Gallardo-Gutiérrez","doi":"10.1112/blms.13159","DOIUrl":"https://doi.org/10.1112/blms.13159","url":null,"abstract":"We address the existence of non-trivial closed invariant subspaces of operators <math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> on Banach spaces whenever their square <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>T</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$T^2$</annotation>\u0000 </semantics></math> have or, more generally, whether there exists a polynomial <math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mtext>deg</mtext>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>)</mo>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$mbox{deg}(p)geqslant 2$</annotation>\u0000 </semantics></math> such that the lattice of invariant subspaces of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>(</mo>\u0000 <mi>T</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$p(T)$</annotation>\u0000 </semantics></math> is non-trivial. In the Hilbert space setting, the <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>T</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$T^2$</annotation>\u0000 </semantics></math>-problem was posed by Halmos in the seventies and in 2007, Foias, Jung, Ko and Pearcy conjectured it could be equivalent to the Invariant Subspace Problem.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 12","pages":"3681-3688"},"PeriodicalIF":0.8,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142851507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Multiplicity results for nonlocal critical elliptic problems 非局部临界椭圆问题的多重性结果

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-09-23 DOI: 10.1112/blms.13156

Said El Manouni, Kanishka Perera

{"title":"Multiplicity results for nonlocal critical elliptic problems","authors":"Said El Manouni, Kanishka Perera","doi":"10.1112/blms.13156","DOIUrl":"https://doi.org/10.1112/blms.13156","url":null,"abstract":"We prove new multiplicity results for some nonlocal critical growth elliptic problems in bounded domains. More specifically, we show that the problems considered here have arbitrarily many solutions for all sufficiently large values of a certain parameter <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$lambda > 0$</annotation>\u0000 </semantics></math>. In particular, the number of solutions goes to infinity as <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$lambda rightarrow infty$</annotation>\u0000 </semantics></math>. We also give an explicit lower bound on <math>\u0000 <semantics>\u0000 <mi>λ</mi>\u0000 <annotation>$lambda$</annotation>\u0000 </semantics></math> in order to have a given number of solutions. This lower bound is in terms of a sequence of eigenvalues of the associated nonlocal elliptic operator. The proofs are based on an abstract critical point theorem.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 12","pages":"3643-3651"},"PeriodicalIF":0.8,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Actions on classifiable C*-algebras without equivariant property (SI) 无等变性质可分类C*-代数上的作用

IF 0.8 3区数学

Bulletin of the London Mathematical Society Pub Date : 2024-09-21 DOI: 10.1112/blms.13154

Eusebio Gardella, Julian Kranz, Andrea Vaccaro

引用次数: 0