Annals of Functional Analysis最新文献

{"title":"Triangular-(theta ) summability of double Fourier series on quantum tori","authors":"Yong Jiao,&nbsp;Tiantian Zhao,&nbsp;Dejian Zhou","doi":"10.1007/s43034-024-00376-3","DOIUrl":"10.1007/s43034-024-00376-3","url":null,"abstract":"<div><p>We study the triangular <span>(theta )</span>-mean of the partial sums of <span>(f in L_{p}({mathbb {T}}_{q}^{2}))</span> and prove the following noncommutative weak and strong type maximal inequalities: </p><div><div><span>$$begin{aligned} Vert (sigma _n^{Delta ,theta }(f))_{nge 1}Vert _{Lambda _{1,infty }({mathbb {T}}_q^2,ell _{infty })}le c_theta Vert fVert _{L_1({mathbb {T}}_{q}^2)},quad p=1 end{aligned}$$</span></div></div><p>and </p><div><div><span>$$begin{aligned} left| left( sigma _{n}^{Delta ,theta }(f)right) _{n ge 1}right| _{L_p({mathbb {T}}_q^2, ell _{infty })} le c_{p, theta }Vert fVert _{L_p({mathbb {T}}_q^2)},quad 1&lt;p&lt;infty , end{aligned}$$</span></div></div><p>where <span>({mathbb {T}}_{q}^{2})</span> is a 2-dimensional quantum torus. As a consequence, we obtain the bilateral almost uniform convergence of <span>(sigma _n^{Delta ,theta }(f))</span> provided <span>(f in L_{p}({mathbb {T}}_{q}^{2}).)</span></p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775687","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}

{"title":"Extremals of singular Hardy–Trudinger–Moser inequality with remainder terms on unit disc","authors":"Weiwei Wang","doi":"10.1007/s43034-024-00377-2","DOIUrl":"10.1007/s43034-024-00377-2","url":null,"abstract":"<div><p>Let <span>(Bsubset {mathbb {R}}^2)</span> be the unit disc, and <span>({mathcal {H}})</span> be the completion of <span>(C_0^infty ({B}))</span> under the norm </p><div><div><span>$$begin{aligned} Vert uVert _{{mathcal {H}}}=Bigg (int _{{B}}|nabla u|^2 {textrm{d}}x- int _{{B}}frac{u^2}{(1-|x|^2)^2}{textrm{d}}xBigg )^{frac{1}{2}}. end{aligned}$$</span></div></div><p>We derive in this paper extremals of singular Hardy–Trudinger–Moser inequality with remainder terms on <i>B</i> using the method of blow-up analysis and rearrangement argument: suppose <span>(0&lt;t&lt;2,)</span> there exists a constant <span>(delta _0&gt;0)</span> such that for <span>(gamma le 4pi (1-t/2)+delta _0)</span> the supremum </p><div><div><span>$$begin{aligned} sup _{uin {mathcal {H}},Vert uVert _{{mathcal {H}}}le 1}int _{{B}}frac{{textrm{e}}^{4pi (1-t/2)u^2}-gamma u^2}{|x|^t} {textrm{d}}x end{aligned}$$</span></div></div><p>can be attained. This extends results of Wang and Ye (Adv Math 230:294–320, 2012) and Yin (Bull Iran Math Soc 49, 2023).</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141715896","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}

{"title":"Criterion for ellipticity on Heisenberg group","authors":"Dmitriy Zanin","doi":"10.1007/s43034-024-00375-4","DOIUrl":"10.1007/s43034-024-00375-4","url":null,"abstract":"<div><p>We provide a semi-constructive criterion for ellipticity of the differential operator on the Heisenberg group <span>(mathbb {H}^1.)</span></p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00375-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614069","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}

{"title":"A universal property of semigroup (C^*)-algebras generated by cones in groups of rationals","authors":"Renat Gumerov,&nbsp;Anatoliy Kuklin,&nbsp;Ekaterina Lipacheva","doi":"10.1007/s43034-024-00374-5","DOIUrl":"10.1007/s43034-024-00374-5","url":null,"abstract":"<div><p>The article deals with the reduced semigroup <span>(C^*)</span>-algebras for the positive cones in ordered abelian groups. These <span>(C^*)</span>-algebras are generated by the regular isometric representations of the cones. Using the universal property of the isometric representations for the positive cones, we treat the reduced semigroup <span>(C^*)</span>-algebras as the universal <span>(C^*)</span>-algebras which are defined by sets of generators subject to relations. For arbitrary sequences of prime numbers, we consider the ordered groups of rational numbers determined by these sequences and the reduced semigroup <span>(C^*)</span>-algebras of the positive cones in these groups. It is shown that such an algebra can be characterized as a universal <span>(C^*)</span>-algebra generated by a countable set of isometries subject to polynomial relations associated with a sequence of prime numbers.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141571684","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}

{"title":"Complex interpolation between noncommutative martingale BMO spaces and Hardy–Orlicz spaces","authors":"Mixuan Hou,&nbsp;Cuiting Li,&nbsp;Guangheng Xie,&nbsp;Yahui Zuo","doi":"10.1007/s43034-024-00373-6","DOIUrl":"10.1007/s43034-024-00373-6","url":null,"abstract":"<div><p>Let <span>(mathcal {M})</span> be a semifinite von Neumann algebra and <span>((mathcal {M}_n)_{nge 0})</span> a nondecreasing filtration of von Neumann subalgebras of <span>(mathcal {M})</span>. Suppose that <span>(Phi )</span> is a <i>p</i>-convex and <i>q</i>-concave Orlicz function with <span>(1&lt; ple q &lt;infty )</span>. In this paper, we establish the complex interpolation between the column martingale little BMO space <span>(textrm{bmo}^c(mathcal {M}))</span> and the noncommutative column conditioned martingale Hardy–Orlicz space <span>(h_{Phi }^c(mathcal {M}))</span> associated with the filtration <span>((mathcal {M}_n)_{nge 0})</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551645","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}

{"title":"Norm inequalities for the iterated perturbations of Laplace transformers generated by accretive (scriptstyle N)-tuples of operators in Q and Q* ideals of compact operators","authors":"Danko R. Jocić,&nbsp;Zora Lj. Golubović,&nbsp;Mihailo Krstić,&nbsp;Stevan Milašinović","doi":"10.1007/s43034-024-00364-7","DOIUrl":"10.1007/s43034-024-00364-7","url":null,"abstract":"<div><p>Let <span>(Phi ,Psi )</span> be symmetrically norming (s.n.) functions, <img> and <span>({{{{mathscr {L}}}}};![mu ;!]Delta _{scriptscriptstyle A;!,B}X;!{mathop {=}limits ^{tiny {text {def}}}};!{{{{mathscr {L}}}}};X;!{mathop {=}limits ^{tiny {text {def}}}};!int _{{{mathbb {R}}}_+}!e^{!-tA}Xe^{!-tB};!dmu (t))</span> denotes the Laplace transformer generated by the generalized derivation <img> where <span>(mu )</span> is a Borel probability measure on <img> If both pairs <img> consist of mutually commuting accretive operators, such that both <span>(C;!-A)</span> and <span>(D-B)</span> are accretive and <img> for some <img>, then <span>({{{{mathscr {L}}}}};![mu ;!]Delta _{scriptscriptstyle A^{;!*}!!,A}^{};!(I)-{{{{mathscr {L}}}}};![mu ;!]Delta _{scriptscriptstyle C^*!!,C}^{};!(I);!geqslant ;!0,{{{{mathscr {L}}}}};![mu ;!]Delta _{scriptscriptstyle B;!,B^*}^{};!(I)-{{{{mathscr {L}}}}};![mu ;!]Delta _{scriptscriptstyle D;!,D^*}^{};!(I);!geqslant ;!0)</span> and </p><div><div><span>$$begin{aligned}&amp;;!bigl vert {bigl vert {!sqrt{C^*!;!+!C!-A^*!;!-!A}bigl ({{{{{mathscr {L}}}}};![mu ;!]Delta _{scriptscriptstyle A;!,B}X-{{{{mathscr {L}}}}};![mu ;!]Delta _{scriptscriptstyle C;!,D}X}bigr )!sqrt{D!+!;!D^*!-!B-!B^*};!}bigr vert }bigr vert _Psi &amp;leqslant ;!Bigl vert Bigl vert {textstyle sqrt{{{{{mathscr {L}}}}};![mu ;!]Delta _{scriptscriptstyle A^{;!*}!!,A}^{};!(I)-{{{{mathscr {L}}}}};![mu ;!]Delta _{scriptscriptstyle C^*!!,C}^{};!(I)};!({AX!+!XB-CX!-!XD})}Bigr .Bigr .&amp;times Bigl .Bigl .{!sqrt{{{{{mathscr {L}}}}};![mu ;!]Delta _{scriptscriptstyle B;!,B^*}^{};!(I)-{{{{mathscr {L}}}}};![mu ;!]Delta _{scriptscriptstyle D;!,D^*}^{};!(I)}}Bigr vert Bigr vert _Psi , end{aligned}$$</span></div></div><p>holds under any of the following conditions: (a) if <img> (b) if <img> for some <span>(pgeqslant 2,{ L^{;!2};!(;!{{{mathbb {R}}}_+};!,mu )})</span> is separable and at least one of pairs (<i>A</i>, <i>C</i>) or (<i>B</i>, <i>D</i>) consists of normal operators, (c) if both pairs (<i>A</i>, <i>C</i>) and (<i>B</i>, <i>D</i>) consist of normal operators. Above, <span>({Phi ^{^(;!!^{p};!!^)}}!)</span> denotes (the degree) <i>p</i>-modified s.n. function <span>(Phi )</span> and <span>({Phi ^{{^(;!!^{p};!!^)}^{_*}}}!!)</span> is the dual s.n. function for <span>({Phi ^{^(;!!^{p};!!^)}}!.)</span> Moreover, the aforementioned inequality is generalized to the iterated perturbations of Laplace transformers, and the alternative inequalities are given for Q norms as well. These inequalities also generalize some previously obtained results.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141345490","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}

{"title":"Crossed product C(^*)-algebras associated with p-adic multiplication","authors":"Shelley Hebert,&nbsp;Slawomir Klimek,&nbsp;Matt McBride,&nbsp;J. Wilson Peoples","doi":"10.1007/s43034-024-00372-7","DOIUrl":"10.1007/s43034-024-00372-7","url":null,"abstract":"<div><p>We introduce and investigate some examples of C<span>(^*)</span>-algebras which are related to multiplication maps in the ring of <i>p</i>-adic integers. We find ideals within these algebras and use the corresponding short exact sequences to compute the <i>K</i>-theory.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141349677","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}

{"title":"On the symplectic self-adjointness and residual spectral emptiness of upper triangular Hamiltonian operator matrices","authors":"Jie Liu,&nbsp;Guohai Jin,&nbsp;Buhe Eerdun","doi":"10.1007/s43034-024-00367-4","DOIUrl":"10.1007/s43034-024-00367-4","url":null,"abstract":"<div><p>This paper deals with the symplectic self-adjointness and residual spectral emptiness of upper triangular Hamiltonian operator matrices <span>(H=left( {begin{matrix}A&amp;{}B 0&amp;{}-A^*end{matrix}}right) )</span>. First, for symplectic self-adjoint Hamiltonian operator <i>H</i>, based on detailed classification of point spectrum <span>(sigma _p(H))</span> and residual spectrum <span>(sigma _r(H))</span>, the symmetry about imaginary axis is given between <span>(sigma _p(H))</span>, <span>(sigma _r(H))</span>, deficiency spectrum <span>(sigma _{delta }(H))</span>, compression spectrum <span>(sigma _mathrm{{com}}(H))</span> and approximate point spectrum <span>(sigma _mathrm{{app}}(H))</span>. Second, by means of the spectral symmetry, the sufficient and necessary conditions are given for <span>(sigma _r(H)=varnothing )</span>, <span>(sigma _{r_1}(H)=varnothing )</span> and <span>(sigma _{r_2}(H)=varnothing )</span>, respectively. Then, for <span>(H=left( {begin{matrix}A&amp;{}B 0&amp;{}-A^*end{matrix}}right) )</span>, it is proved that <i>H</i> is symplectic self-adjoint, if <i>H</i> is defined with diagonal domain <span>({mathcal {D}}(H)={mathcal {D}}(A)oplus {mathcal {D}}(A^*))</span>. Finally, for <span>(H=left( {begin{matrix}A&amp;{}B 0&amp;{}-A^*end{matrix}}right) )</span> defined with diagonal domain, using the space decomposition, the sufficient and necessary conditions for <span>(sigma _r(H)=varnothing )</span> and <span>(sigma _{r_1}(H)=varnothing )</span> are described in detail, respectively, by line operator, null space, and range of inner elements.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00367-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141351225","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}

{"title":"Perturbation formulae for the generalized core–EP inverse","authors":"Dijana Mosić","doi":"10.1007/s43034-024-00371-8","DOIUrl":"10.1007/s43034-024-00371-8","url":null,"abstract":"<div><p>The aim of this paper is to present perturbation formulae and perturbation bounds for the GCEP inverse, gMP inverse and their duals. We also study equivalent conditions for absorption laws of the GCEP inverse, the gMP inverse and their duals and use these results to get perturbation bounds. Applying the GCEP and *GCEP inverses, we introduce two new binary relations and show that they are partial orders on corresponding set.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141362201","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}

{"title":"On m-complex-self-adjoint operators","authors":"Muneo Chō,&nbsp;Ji Eun Lee","doi":"10.1007/s43034-024-00349-6","DOIUrl":"10.1007/s43034-024-00349-6","url":null,"abstract":"<div><p>A linear operator <i>T</i> belonging to the space <span>(mathcal {L}(mathcal {H}))</span> is called as “complex-self-adjoint\" if there exists an antiunitary operator <i>C</i> such that <span>(T^{*} = CTC^{-1})</span>. This paper investigates the spectral characteristics of complex-self-adjoint operators. Additionally, we introduce the notion of <i>m</i>-complex-self-adjoint operators, representing a generalization of complex-self-adjoint operators. Finally, various properties of <i>m</i>-complex-self-adjoint operators are examined.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141362164","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}