Annals of Functional Analysis最新文献

{"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}