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Continuous multiplicative spectral functionals on Hermitian Banach algebras 赫米蒂巴纳赫代数上的连续乘法谱函数
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-06-08 DOI: 10.1007/s43034-024-00369-2
M. Mabrouk, K. Alahmari, R. Brits
{"title":"Continuous multiplicative spectral functionals on Hermitian Banach algebras","authors":"M. Mabrouk,&nbsp;K. Alahmari,&nbsp;R. Brits","doi":"10.1007/s43034-024-00369-2","DOIUrl":"10.1007/s43034-024-00369-2","url":null,"abstract":"<div><p>Let <span>(mathfrak {A})</span> be a unital Hermitian Banach algebra with the spectrum of <span>(ain mathfrak {A})</span> denoted by <span>(sigma _mathfrak {A}(a))</span>. We show that if a continuous and multiplicative function <span>(phi : mathfrak {A}rightarrow mathbb {C})</span> satisfies <span>(phi (a)in sigma (a))</span> for all <span>(ain mathfrak {A})</span>, then <span>(phi )</span> is linear and hence a character of <span>(mathfrak {A})</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141368370","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
Existence of positive solutions to the biharmonic equations in (mathbb {R}^{N}) $$mathbb {R}^{N}$ 中双谐方程正解的存在性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-06-03 DOI: 10.1007/s43034-024-00362-9
Wenbo Wang, Jixiang Ma, Jianwen Zhou
{"title":"Existence of positive solutions to the biharmonic equations in (mathbb {R}^{N})","authors":"Wenbo Wang,&nbsp;Jixiang Ma,&nbsp;Jianwen Zhou","doi":"10.1007/s43034-024-00362-9","DOIUrl":"10.1007/s43034-024-00362-9","url":null,"abstract":"<div><p>This article considers the biharmonic equation </p><div><div><span>$$begin{aligned} Delta ^{2}u=K(x)f(u)quad text {in }~mathbb { R}^{N}. end{aligned}$$</span></div></div><p>Under suitable assumptions, the existence of positive solutions is obtained. The methods used here contain the integral operator and the Schauder fixed point theory. Since the form of fundamental solution of <span>(Delta ^{2}u=0)</span> in <span>(mathbb {R}^{N})</span> depends on <i>N</i>, we divide our discussions into three cases as (a) <span>(N=2)</span>; (b) <span>(N=4)</span>; (c) <span>(N&gt;2)</span> but <span>(Nne 4)</span>. The fundamental solution of <span>(Delta ^{2})</span> plays an essential role in our results.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A new uniform structure for Hilbert (C^*)-modules 希尔伯特 $$C^*$$ 模块的新统一结构
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-06-03 DOI: 10.1007/s43034-024-00368-3
Denis Fufaev, Evgenij Troitsky
{"title":"A new uniform structure for Hilbert (C^*)-modules","authors":"Denis Fufaev,&nbsp;Evgenij Troitsky","doi":"10.1007/s43034-024-00368-3","DOIUrl":"10.1007/s43034-024-00368-3","url":null,"abstract":"<div><p>We introduce and study some new uniform structures for Hilbert <span>(C^*)</span>-modules over a <span>(C^*)</span>-algebra <span>(mathcal {A}.)</span> In particular, we prove that in some cases they have the same totally bounded sets. To define one of them, we introduce a new class of <span>(mathcal {A})</span>-functionals: locally adjointable functionals, which have interesting properties in this context and seem to be of independent interest. A relation between these uniform structures and the theory of <span>(mathcal {A})</span>-compact operators is established.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253043","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
The Livšic function of a homogeneous symmetric operator and the multiplication theorem 同质对称算子的李夫希奇函数和乘法定理
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-06-03 DOI: 10.1007/s43034-024-00370-9
K. A. Makarov, E. Tsekanovskii
{"title":"The Livšic function of a homogeneous symmetric operator and the multiplication theorem","authors":"K. A. Makarov,&nbsp;E. Tsekanovskii","doi":"10.1007/s43034-024-00370-9","DOIUrl":"10.1007/s43034-024-00370-9","url":null,"abstract":"<div><p>This paper presents a solution to the Jørgensen–Muhly problem for a homogeneous symmetric operator with deficiency indices (1, 1) that <b>does not admit</b> a homogeneous self-adjoint extension. Based on the Livšic function approach, we characterize the set of all the solutions of the Jørgensen–Muhly problem up to unitary equivalence and describe the complete set of the corresponding unitary invariants.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253252","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
Ideal spaces of measurable operators affiliated to a semifinite von Neumann algebra. II 隶属于半有限 von Neumann 代数的可测算子的理想空间。二
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-23 DOI: 10.1007/s43034-024-00361-w
A. M. Bikchentaev, M. F. Darwish, M. A. Muratov
{"title":"Ideal spaces of measurable operators affiliated to a semifinite von Neumann algebra. II","authors":"A. M. Bikchentaev,&nbsp;M. F. Darwish,&nbsp;M. A. Muratov","doi":"10.1007/s43034-024-00361-w","DOIUrl":"10.1007/s43034-024-00361-w","url":null,"abstract":"<div><p>Let <span>(tau )</span> be a faithful semifinite normal trace on a von Neumann algebra <span>(mathcal {M})</span>, let <span>(S(mathcal {M}, tau ))</span> be the <span>({}^*)</span>-algebra of all <span>(tau )</span>-measurable operators. Let <span>(mu (t; X))</span> be the generalized singular value function of the operator <span>(X in S(mathcal {M}, tau ))</span>. If <span>(mathcal {E})</span> is a normed ideal space (NIS) on <span>((mathcal {M}, tau ))</span>, then </p><div><div><span>$$begin{aligned} Vert AVert _mathcal {E}le Vert A+textrm{i} BVert _mathcal {E} end{aligned}$$</span></div><div>\u0000 (*)\u0000 </div></div><p>for all self-adjoint operators <span>(A, B in mathcal {E})</span>. In particular, if <span>(A, B in (L_1+L_{infty })(mathcal {M}, tau ))</span> are self-adjoint, then we have the (Hardy–Littlewood–Pólya) weak submajorization, <span>(A preceq _w A+textrm{i}B)</span>. Inequality <span>((*))</span> cannot be extended to the Shatten–von Neumann ideals <span>(mathfrak {S}_p)</span>, <span>( 0&lt; p &lt;1)</span>. Hence, the well-known inequality <span>( mu (t; A) le mu (t; A+textrm{i} B))</span> for all <span>(t&gt;0)</span>, positive <span>(A in S(mathcal {M}, tau ))</span> and self-adjoint <span>( B in S(mathcal {M}, tau ))</span> cannot be extended to all self-adjoint operators <span>(A, B in S(mathcal {M}, tau ))</span>. Consider self-adjoint operators <span>(X, Yin S(mathcal {M}, tau ))</span>, let <i>K</i>(<i>X</i>) be the Cayley transform of <i>X</i>. Then, <span>(mu (t; K(X)-K(Y))le 2 mu (t; X-Y))</span> for all <span>(t&gt;0)</span>. If <span>(mathcal {E})</span> is an <i>F</i>-NIS on <span>((mathcal {M}, tau ))</span> and <span>(X-Yin mathcal {E})</span>, then <span>(K(X)-K(Y)in mathcal {E})</span> and <span>(Vert K(X)-K(Y)Vert _mathcal {E}le 2 Vert X-YVert _mathcal {E})</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141104343","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
Heat expansion and zeta 热膨胀和 zeta
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-23 DOI: 10.1007/s43034-024-00358-5
Alain Connes
{"title":"Heat expansion and zeta","authors":"Alain Connes","doi":"10.1007/s43034-024-00358-5","DOIUrl":"10.1007/s43034-024-00358-5","url":null,"abstract":"<div><p>We compute the full asymptotic expansion of the heat kernel <span>(textrm{Tr}(exp (-tD^2)))</span> where <i>D</i> is, assuming RH, the self-adjoint operator whose spectrum is formed of the imaginary parts of non-trivial zeros of the Riemann zeta function. The coefficients of the expansion are explicit expressions involving Bernoulli and Euler numbers. We relate the divergent terms with the heat kernel expansion of the Dirac square root of the prolate wave operator investigated in our joint work with Henri Moscovici.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151365","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
The lateral order on Köthe–Bochner spaces and orthogonally additive operators 科特-波赫纳空间的侧序和正交相加算子
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-23 DOI: 10.1007/s43034-024-00360-x
Marat Pliev, Nariman Abasov, Nonna Dzhusoeva
{"title":"The lateral order on Köthe–Bochner spaces and orthogonally additive operators","authors":"Marat Pliev,&nbsp;Nariman Abasov,&nbsp;Nonna Dzhusoeva","doi":"10.1007/s43034-024-00360-x","DOIUrl":"10.1007/s43034-024-00360-x","url":null,"abstract":"<div><p>In this paper, we introduce a new class of regular orthogonally additive operators defined on a lattice-normed space <span>((mathcal {X},E))</span> and taking values in a vector lattice <i>F</i>. We show that the vector space <span>(mathcal{O}mathcal{A}_r(mathcal {X},F))</span> of all regular orthogonally additive operators from a <i>d</i>-decomposable lattice-normed space <span>((mathcal {X},E))</span> to a Dedekind complete vector lattice <i>F</i> is a Dedekind complete vector lattice and the lattice operations can be calculated by the Riesz–Kantorovich formulas. We find necessary and sufficient conditions for an orthogonally additive operator <span>(T:mathcal {X}rightarrow F)</span> to be dominated and obtain a criterion of the positivity of a nonlinear superposition operator <span>(T_N:E(X)rightarrow E)</span> defined on Köthe–Bochner space <i>E</i>(<i>X</i>) and taking values in Köthe-*Banach space <i>E</i>. Finally, we state some open problems.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141166350","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 functions with traces in Q type spaces related to weights Q 型空间中与权重有关的迹的谐函数
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-17 DOI: 10.1007/s43034-024-00363-8
Shengwen Liu, Chen Zhang, Pengtao Li
{"title":"Harmonic functions with traces in Q type spaces related to weights","authors":"Shengwen Liu,&nbsp;Chen Zhang,&nbsp;Pengtao Li","doi":"10.1007/s43034-024-00363-8","DOIUrl":"10.1007/s43034-024-00363-8","url":null,"abstract":"<div><p>In this article, via a family of convolution operators <span>({phi _t}_{t&gt;0})</span>, we characterize the extensions of a class of <i>Q</i> type spaces <span>(Q^{p,q}_{K,lambda }(mathbb {R}^n))</span> related with weights <span>(K(cdot ))</span>. Unlike the classical <i>Q</i> type spaces which are related with power functions, a general weight function <span>(K(cdot ))</span> is short of homogeneity of the dilation, and is not variable-separable. Under several assumptions on the integrability of <span>(K(cdot ))</span>, we establish a Carleson type characterization of <span>(Q^{p,q}_{K,lambda }(mathbb {R}^n))</span>. We provide several applications. For the spatial dimension <span>(n=1)</span>, such an extension result indicates a boundary characterization of a class of analytic functions on <span>(mathbb R^{2}_{+})</span>. For the case <span>(nge 2)</span>, the family <span>({phi _t}_{t&gt;0})</span> can be seen as a generalization of the fundamental solutions to fractional heat equations, Caffarelli–Silvestre extensions and time-space fractional equations, respectively. Moreover, the boundedness of convolution operators on <span>(Q^{p,q}_{K,lambda }(mathbb {R}^n))</span> is also obtained, including convolution singular integral operators and fractional integral operators.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140965239","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
Variants of 2-local maps on function algebras 函数代数上 2 局部映射的变体
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-15 DOI: 10.1007/s43034-024-00366-5
Liguang Wang, Xueyan Yang, Lei Li
{"title":"Variants of 2-local maps on function algebras","authors":"Liguang Wang,&nbsp;Xueyan Yang,&nbsp;Lei Li","doi":"10.1007/s43034-024-00366-5","DOIUrl":"10.1007/s43034-024-00366-5","url":null,"abstract":"<div><p>We study several variants of 2-local isometries (or algebra isomorphisms) on some function algebras, e.g., Lipschitz algebras, algebras of differential functions, algebras of absolutely continuous functions and algebras of continuous functions with bounded variation. A typical result is this: if <span>(phi )</span> is surjective map between function algebra mentioned above with the property that for any pair <i>f</i>, <i>g</i> there is an algebra isomorphism <span>(phi _{f,g})</span> such that <span>(phi (f)phi (g)=phi _{f,g}(fg))</span>, then <span>(phi )</span> can be written as a weighted composition operator.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972933","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
Generalized Cesàro operator acting on Hilbert spaces of analytic functions 作用于解析函数希尔伯特空间的广义塞萨罗算子
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-05-14 DOI: 10.1007/s43034-024-00365-6
Alejandro Mas, Noel Merchán, Elena de la Rosa
{"title":"Generalized Cesàro operator acting on Hilbert spaces of analytic functions","authors":"Alejandro Mas,&nbsp;Noel Merchán,&nbsp;Elena de la Rosa","doi":"10.1007/s43034-024-00365-6","DOIUrl":"10.1007/s43034-024-00365-6","url":null,"abstract":"<div><p>Let <span>(mathbb {D})</span> denote the unit disc in <span>(mathbb {C})</span>. We define the generalized Cesàro operator as follows: </p><div><div><span>$$begin{aligned} C_{omega }(f)(z)=int _0^1 f(tz)left( frac{1}{z}int _0^z B^{omega }_t(u),textrm{d}uright) ,omega (t)textrm{d}t, end{aligned}$$</span></div></div><p>where <span>({B^{omega }_zeta }_{zeta in mathbb {D}})</span> are the reproducing kernels of the Bergman space <span>(A^{2}_{omega })</span> induced by a radial weight <span>(omega )</span> in the unit disc <span>(mathbb {D})</span>. We study the action of the operator <span>(C_{omega })</span> on weighted Hardy spaces of analytic functions <span>(mathcal {H}_{gamma })</span>, <span>(gamma &gt;0)</span> and on general weighted Bergman spaces <span>(A^{2}_{mu })</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00365-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925514","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
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