Annals of Functional Analysis最新文献

{"title":"Beurling quotient subspaces for covariant representations of product systems","authors":"Azad Rohilla,&nbsp;Harsh Trivedi,&nbsp;Shankar Veerabathiran","doi":"10.1007/s43034-023-00301-0","DOIUrl":"10.1007/s43034-023-00301-0","url":null,"abstract":"<div><p>Let <span>((sigma , V^{(1)}, dots , V^{(k)}))</span> be a pure doubly commuting isometric representation of the product system <span>({mathbb {E}})</span> on a Hilbert space <span>({mathcal {H}}_{V}.)</span> A <span>(sigma )</span>-invariant subspace <span>({mathcal {K}})</span> is said to be <i>Beurling quotient subspace</i> of <span>({mathcal {H}}_{V})</span> if there exist a Hilbert space <span>({mathcal {H}}_W,)</span> a pure doubly commuting isometric representation <span>((pi , W^{(1)}, dots , W^{(k)}))</span> of <span>({mathbb {E}})</span> on <span>({mathcal {H}}_W)</span> and an isometric multi-analytic operator <span>(M_Theta :{{mathcal {H}}_W} rightarrow {mathcal {H}}_{V})</span>, such that </p><div><div><span>$$begin{aligned} {mathcal {K}}={mathcal {H}}_{V}ominus M_{Theta }{mathcal {H}}_W, end{aligned}$$</span></div></div><p>where <span>(Theta : {mathcal {W}}_{{mathcal {H}}_W} rightarrow {mathcal {H}}_{V} )</span> is an inner operator and <span>({mathcal {W}}_{{mathcal {H}}_W})</span> is the generating wandering subspace for <span>((pi , W^{(1)}, dots , W^{(k)}).)</span> In this article, we prove the following characterization of the Beurling quotient subspaces: A subspace <span>({mathcal {K}})</span> of <span>({mathcal {H}}_{V})</span> is a Beurling quotient subspace if and only if </p><div><div><span>$$begin{aligned}&amp;(I_{E_{j}}otimes ( (I_{E_{i}}otimes P_{{mathcal {K}}}) - widetilde{T}^{(i) *}widetilde{T}^{(i)}))(t_{i,j} otimes I_{{mathcal {H}}_{V}})&amp;(I_{E_{i}}otimes ( (I_{E_{j}}otimes P_{{mathcal {K}}})- widetilde{T}^{(j) *}widetilde{T}^{(j)}))=0, end{aligned}$$</span></div></div><p>where <span>(widetilde{T}^{(i)}:=P_{{mathcal {K}}}widetilde{V}^{(i)} (I_{E_{i}} otimes P_{{mathcal {K}}}))</span> and <span>( 1 le i,jle k.)</span> As a consequence, we derive a concrete regular dilation theorem for a pure, completely contractive covariant representation <span>((sigma , V^{(1)}, dots , V^{(k)}))</span> of <span>({mathbb {E}})</span> on a Hilbert space <span>({mathcal {H}}_{V})</span> which satisfies Brehmer–Solel condition and using it and the above characterization, we provide a necessary and sufficient condition that when a completely contractive covariant representation is unitarily equivalent to the compression of the induced representation on the Beurling quotient subspace. Further, we study the relation between Sz. Nagy–Foias-type factorization of isometric multi-analytic operators and joint invariant subspaces of the compression of the induced representation on the Beurling quotient subspace.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-023-00301-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50450577","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":"On the Schauder fixed point property II","authors":"Khadime Salame","doi":"10.1007/s43034-023-00300-1","DOIUrl":"10.1007/s43034-023-00300-1","url":null,"abstract":"<div><p>The Schauder fixed point property (<b>F</b>) was introduced and studied by Lau and Zhang as a semigroup formulation in the general setting of convex spaces of the well-known Schauder fixed point theorem in Banach spaces. What amenability property should possess a semigroup or a topological group to satisfy the Schauder fixed point property. Recently, the author provided a partial answer to that question and as a sequel, it is the purpose of this paper to study in more deep this problem. Our main result establishes that for a compact semitopological semigroup <i>S</i> we have: LUC(<i>S</i>) is left amenable if, and only if, <i>S</i> has the fixed point property (<b>F</b>). Furthermore, we also prove that totally bounded topological groups, semitopological groups <i>S</i> with the property that LUC(<i>S</i>) <span>(subset )</span><span>({textrm{aa}})</span>(<i>S</i>), and strongly left amenable semitopological semigroups, possess all the Schauder fixed point property.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50504466","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":"A non-trivial solution for a p-Schrödinger–Kirchhoff-type integro-differential system by non-smooth techniques","authors":"Juan Mayorga-Zambrano,&nbsp;Daniel Narváez-Vaca","doi":"10.1007/s43034-023-00299-5","DOIUrl":"10.1007/s43034-023-00299-5","url":null,"abstract":"<div><p>We consider the integro-differential system <span>((textrm{P}_m))</span>: </p><div><div><span>$$begin{aligned} - left( a_k+b_k left( displaystyle int _{{mathbb {R}}^{N}} |nabla u_k|^{p} dx right) ^{p-1} right) Delta _{p} u_k + V(x) |u_k|^{p-2} u_k = partial _{k} F(u_1,ldots ,u_m), end{aligned}$$</span></div></div><p>where <span>(xin {mathbb {R}}^N)</span>, <span>(a_k&gt;0)</span>, <span>(b_kge 0)</span>, <span>(Nge 2)</span> and <span>(1&lt;p&lt;N)</span>, <span>(u_k in textrm{W}^{1,p}({mathbb {R}}^{N}))</span>, for <span>(k=1,ldots ,m)</span>. By <span>(partial _{k} F(u_1,ldots ,u_m),)</span> it is denoted the <i>k</i>-th partial generalized gradient in the sense of Clarke. The potential <span>(Vin textrm{C} left( {mathbb {R}}^N right) )</span> verifies <span>(inf (V)&gt;0)</span> and a coercivity property introduced by Bartsch et al. The coupling function <span>(F:{mathbb {R}}^mlongrightarrow {mathbb {R}})</span> is locally Lipschitz and verifies conditions introduced by Duan and Huang. By applying tools from the non-smooth critical point theory, we prove the existence of a non-trivial mountain pass solution of <span>((textrm{P}_m))</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50494286","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":"Preduals of variable Morrey–Campanato spaces and boundedness of operators","authors":"Ciqiang Zhuo","doi":"10.1007/s43034-023-00298-6","DOIUrl":"10.1007/s43034-023-00298-6","url":null,"abstract":"<div><p>Let <span>(p(cdot ): {mathbb {R}}^nrightarrow (1,infty ))</span> be a variable exponent, such that the Hardy–Littlewood maximal operator is bounded on the variable exponent Lebesgue space <span>(L^{p(cdot )}({mathbb {R}}^n),)</span> and <span>(phi : {mathbb {R}}^ntimes (0,infty )rightarrow (0,infty ))</span> be a function satisfying some conditions. In this article, we give some properties of variable Campanato spaces <span>({mathcal {L}}_{p(cdot ),phi ,d}({mathbb {R}}^n),)</span> with a non-negative integer <i>d</i>,  and variable Morrey spaces <span>(L_{p(cdot ),phi }({mathbb {R}}^n),)</span> and then establish their predual spaces. As an application of duality obtained in this article, we consider the boundedness of singular integral operators on variable Morrey spaces and their predual spaces.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44406462","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":"Refinements of the Cauchy–Schwarz inequality in pre-Hilbert C∗documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$C^*$$en","authors":"A. Zamani","doi":"10.1007/s43034-023-00296-8","DOIUrl":"https://doi.org/10.1007/s43034-023-00296-8","url":null,"abstract":"","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43400128","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":"Refinements of the Cauchy–Schwarz inequality in pre-Hilbert (C^*)-modules and their applications","authors":"Ali Zamani","doi":"10.1007/s43034-023-00296-8","DOIUrl":"10.1007/s43034-023-00296-8","url":null,"abstract":"<div><p>New extensions of the Cauchy–Schwarz inequality in the framework of pre-Hilbert <span>(C^*)</span>-modules are given. An application to the numerical radius in <span>(C^*)</span>-algebras is also provided.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-023-00296-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50517411","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":"Rough Hausdorff operators on Lebesgue spaces with variable exponent","authors":"Ziwei Li,&nbsp;Jiman Zhao","doi":"10.1007/s43034-023-00293-x","DOIUrl":"10.1007/s43034-023-00293-x","url":null,"abstract":"<div><p>In this paper, we study rough Hausdorff operators on variable exponent Lebesgue spaces in the setting of the Heisenberg group. We prove the boundedness of rough Hausdorff operators by giving some sufficient conditions.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43214930","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":"Weighted holomorphic mappings attaining their norms","authors":"A. Jiménez-Vargas","doi":"10.1007/s43034-023-00297-7","DOIUrl":"10.1007/s43034-023-00297-7","url":null,"abstract":"<div><p>Given an open subset <i>U</i> of <span>({mathbb {C}}^n,)</span> a weight <i>v</i> on <i>U</i> and a complex Banach space <i>F</i>,  let <span>(mathcal {H}_v(U,F))</span> denote the Banach space of all weighted holomorphic mappings <span>(f:Urightarrow F,)</span> under the weighted supremum norm <span>(left| fright| _v:=sup left{ v(z)left| f(z)right| :zin Uright} .)</span> We prove that the set of all mappings <span>(fin mathcal {H}_v(U,F))</span> that attain their weighted supremum norms is norm dense in <span>(mathcal {H}_v(U,F),)</span> provided that the closed unit ball of the little weighted holomorphic space <span>(mathcal {H}_{v_0}(U,F))</span> is compact-open dense in the closed unit ball of <span>(mathcal {H}_v(U,F).)</span> We also prove a similar result for mappings <span>(fin mathcal {H}_v(U,F))</span> such that <i>vf</i> has a relatively compact range.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-023-00297-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47439874","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":"Noncommutative Pick–Julia theorems for generalized derivations in Q, Q∗documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$","authors":"Danko R. Jocić","doi":"10.1007/s43034-023-00291-z","DOIUrl":"https://doi.org/10.1007/s43034-023-00291-z","url":null,"abstract":"","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48800703","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":"Noncommutative Pick–Julia theorems for generalized derivations in Q, Q(^*) and Schatten–von Neumann ideals of compact operators","authors":"Danko R. Jocić","doi":"10.1007/s43034-023-00291-z","DOIUrl":"10.1007/s43034-023-00291-z","url":null,"abstract":"<div><p>If <i>C</i> and <i>D</i> are strictly accretive operators on <span>({mathcal {H}})</span> and at least one of them is normal, such that <span>(CX!-!XDin { {{{varvec{{mathcal {C}}}}}}_{Psi }({mathcal {H}})})</span> for some <span>(Xin { {{{varvec{{mathcal {B}}}}}}({mathcal H})})</span> and <span>(Q^*)</span> symmetrically norming function <span>(Psi ,)</span> then for all holomorphic functions <i>h</i>,  mapping the open right half (complex) plane into itself, we have <span>(h( C,!)X!-!Xh(D)in { {{{varvec{{mathcal {C}}}}}}_{Psi }({mathcal {H}})},)</span> satisfying </p><div><div><span>$$begin{aligned}&amp;bigl vert {,!bigl vert {(C^*!+C)^{ 1/2}bigl ({h( C,!){}X!-!Xh(D)!,!}bigr )(D+D^*!,!)^{ 1/2}}bigr vert ,!}bigr vert _Psi &amp;leqslant bigl vert {,!bigl vert {bigl ({h( C,!){}^*!+h( C,!){}!,!}bigr )^{ 1/2}{({ CX!-!XD})} bigl ({h(D)+h(D)^*!,!}bigr )^{ 1/2}}bigr vert ,!}bigr vert _Psi . end{aligned}$$</span></div></div><p>If <span>(1leqslant q,r,sleqslant {+infty })</span> and <span>(pgeqslant 2,A,B,Xin { {{{varvec{{mathcal {B}}}}}}({mathcal H})})</span> and <i>A</i>, <i>B</i> are strict contractions satisfying the condition <span>(AX!-!XBin { {{{varvec{{mathcal {C}}}}}}_{s}({mathcal {H}})},)</span> then for all holomorphic functions <i>g</i>,  mapping the open unit disc into the open right half (complex) plane, <span>(g(A)X!-!Xg(B)in { {{{varvec{{mathcal {C}}}}}}_{s}({mathcal {H}})},)</span> satisfying Schatten–von Neumann s-norms <span>((vert {;!vert {cdot }vert ;!}vert _s))</span> inequality </p><div><div><span>$$begin{aligned}&amp;,!Bigl vert !,!Bigl vert {bigl vert {!,!bigl ({g(A)^{*}!+g(A)!,!}bigr )^frac{1}{2}!{({I!-!A^{*}!A})}^frac{1}{2}!,!}bigr vert ^{!frac{1}{q}-1} !,!{({I!-!A^{*}!A})}^frac{1}{2}!bigl ({g(A)X!-!Xg(B)!,!}bigr )}Bigr .Bigr .&amp;times Bigl .Bigl .{{({I!-BB^*!,!})}^frac{1}{2}!bigl vert {!,!bigl ({g(B)+g(B)^{*}!,!}bigr )^frac{1}{2}!{({I!-BB^*!,!})}^frac{1}{2}!,!}bigr vert ^{!frac{1}{r}-1}!,!}Bigr vert !,!Bigr vert _s leqslant&amp;,!Bigl vert !,!Bigl vert {bigl vert {!,!bigl ({g(A)^{*}!+g(A)!,!}bigr )^frac{1}{2}!{({I!-!AA^{*}!,!})}^frac{1}{2}!,!}bigr vert ^frac{1}{q} {({I-AA^*!,!})}^{!,!-frac{1}{2}}!,!{({AX!-!XB})}}Bigr .Bigr .&amp;times Bigl .Bigl .{{({I-B^*!B})}^{!,!-frac{1}{2}}!,!bigl vert {!,!bigl ({g(B)+g(B)^{*} !,!}bigr )^frac{1}{2} !{({I-B^*! B})}^frac{1}{2}!,!}bigr vert ^frac{1}{r}!,!}Bigr vert !,!Bigr vert _s. end{aligned}$$</span></div></div><p>Other variants of some new Pick–Julia-type norm and operator inequalities are also obtained, they both complement the well-known Pick–Julia theorems for operators, obtained by Ky Fan, Ando, and Author, and they also extend these theorems to the field of norm ideals of compact operators, including Schatten–von Neumann ideals.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-023-00291-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50501821","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}