Annals of Functional Analysis最新文献

{"title":"Dixmier-type traces on symmetric spaces associated with semifinite von Neumann algebras","authors":"Galina Levitina,&nbsp;Alexandr Usachev","doi":"10.1007/s43034-024-00343-y","DOIUrl":"10.1007/s43034-024-00343-y","url":null,"abstract":"<div><p>We prove that a normalised linear functional on certain symmetric spaces associated with a semifinite von Neumann algebra, respects tail majorisation if and only if it is a Dixmier-type trace.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586699","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":"New properties and existence of exact phase-retrievable g-frames","authors":"Miao He,&nbsp;Jingsong Leng","doi":"10.1007/s43034-024-00345-w","DOIUrl":"10.1007/s43034-024-00345-w","url":null,"abstract":"<div><p>Due to the frame elements of the g-frames being operators, it has many differences from traditional frames. Hence some new characterizations of exact phase-retrievable g-frames from the perspective of operator theory are mainly discussed in this paper. Firstly, we find that for an exact phase-retrievable g-frame, its canonical dual frame will maintain the exact phase-retrievability. Then the stability of the exact phase-retrievability is discussed. More specifically, an exact phase-retrievable g-frame is still exact phase-retrievable after a small disturbance can be obtained in this paper. In addition, we show that the direct sum of two g-frames which have the exact PR-redundancy property also have the exact PR-redundancy property. With the help of these results, the existence of the exact phase-retrievable g-frames is discussed. We prove that for the real Hilbert space case, an exact phase-retrievable g-frame of length <i>N</i> exists for every <span>(2n-1le N le frac{n(n+1)}{2}.)</span></p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586698","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":"Normalized solutions of linear and nonlinear coupled Choquard systems with potentials","authors":"Zhenyu Guo,&nbsp;Wenyan Jin","doi":"10.1007/s43034-024-00348-7","DOIUrl":"10.1007/s43034-024-00348-7","url":null,"abstract":"<div><p>In this paper, we study Choquard systems with linear and nonlinear couplings with different potentials under the <span>(L^2)</span>-constraint. We use Ekland variational principle to prove this system has a normalized radially symmetric solution for <span>(L^2)</span>-subcritical case when the dimension is greater than or equal to 2 without potentials. In addition, a positive solution with prescribed <span>(L^2)</span>-constraint under some appropriate assumptions with the potentials was obtained. The proof is based on the refined energy estimates.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586841","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 decomposability for sums of complex symmetric operators","authors":"Sungeun Jung","doi":"10.1007/s43034-024-00342-z","DOIUrl":"10.1007/s43034-024-00342-z","url":null,"abstract":"<div><p>In this paper, we study decomposability for sums of complex symmetric operators. As applications, we consider decomposable operator matrices.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586700","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":"Some converse problems on the g-Drazin invertibility in Banach algebras","authors":"Honglin Zou","doi":"10.1007/s43034-024-00344-x","DOIUrl":"10.1007/s43034-024-00344-x","url":null,"abstract":"<div><p>The main purpose of this paper is to investigate the converse problems of some well-known results related to the generalized Drazin (g-Drazin for short) inverse in Banach algebras. Let <span>({mathcal {A}})</span> be a Banach algebra and <span>(a,bin {mathcal {A}})</span>. First, we give the relationship between the Drazin (g-Drazin, group) invertibility of <i>a</i>, <i>b</i> and that of the sum <span>(a+b)</span> under certain conditions. Then, for a given polynomial <span>(f(x)in {mathbb {C}}[x])</span>, the g-Drazin invertibility of <i>f</i>(<i>a</i>), <span>(f(a^{d}))</span>, <i>f</i>(<i>ab</i>), <span>(f(1-ab))</span> and <span>(f(a+b))</span> are investigated.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586697","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":"An extension of the weighted geometric mean in unital JB-algebras","authors":"A. G. Ghazanfari,&nbsp;S. Malekinejad,&nbsp;M. Sababheh","doi":"10.1007/s43034-024-00330-3","DOIUrl":"10.1007/s43034-024-00330-3","url":null,"abstract":"<div><p>Let <span>({mathcal {A}})</span> be a unital <i>JB</i>-algebra and <span>(A,Bin {mathcal {A}})</span>. The weighted geometric mean <span>(Asharp _r B)</span> for <span>(A,Bin {mathcal {A}})</span> has been recently defined for <span>(rin [0,1].)</span> In this work, we extend the weighted geometric mean <span>(Asharp _r B)</span>, from <span>(rin [0,1])</span> to <span>(rin (-1, 0)cup (1, 2))</span>. We will notice that many results will be reversed when the domain of <i>r</i> change from [0, 1] to <span>((-1,0))</span> or (1, 2). We also introduce the Heinz and Heron means of elements in <span>({mathcal {A}})</span>, and extend some known inequalities involving them.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586844","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":"Geometric constant for quantifying the difference between angular and skew angular distances in Banach spaces","authors":"Yuankang Fu,&nbsp;Yongjin Li","doi":"10.1007/s43034-024-00341-0","DOIUrl":"10.1007/s43034-024-00341-0","url":null,"abstract":"<div><p>This article is devoted to introduce a new geometric constant called Dehghan–Rooin constant, which quantifies the difference between angular and skew angular distances in Banach spaces. We quantify the characterization of uniform non-squareness in terms of Dehghan–Rooin constant. The relationships between Dehghan–Rooin constant and uniform convexity, Dehghan-Rooin constant and uniform smoothness are also studied. Moreover, some new sufficient conditions for uniform normal structure are also established in terms of Dehghan–Rooin constant.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586695","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":"Hölder continuity of the gradients for non-homogenous elliptic equations of p(x)-Laplacian type","authors":"Fengping Yao","doi":"10.1007/s43034-024-00340-1","DOIUrl":"10.1007/s43034-024-00340-1","url":null,"abstract":"<div><p>The main goal of this paper is to discuss the local Hölder continuity of the gradients for weak solutions of the following non-homogenous elliptic <i>p</i>(<i>x</i>)-Laplacian equations of divergence form </p><div><div><span>$$begin{aligned} text {div} left( left( A(x) nabla u(x) cdot nabla u(x) right) ^{frac{p(x)-2}{2}} A(x) nabla u(x) right) = text {div} left( |textbf{f}(x) |^{p(x)-2} textbf{f}(x) right) ~~ text{ in }~ Omega , end{aligned}$$</span></div></div><p>where <span>(Omega subset mathbb {R}^{n})</span> is an open bounded domain for <span>(n ge 2)</span>, under some proper non-Hölder conditions on the variable exponents <i>p</i>(<i>x</i>) and the coefficients matrix <i>A</i>(<i>x</i>).</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586842","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":"Martingale Hardy–Orlicz-amalgam spaces","authors":"Libo Li,&nbsp;Kaituo Liu,&nbsp;Yao Wang","doi":"10.1007/s43034-024-00338-9","DOIUrl":"10.1007/s43034-024-00338-9","url":null,"abstract":"<div><p>In this article, the authors first introduce a class of Orlicz-amalgam spaces, which defined on a probabilistic setting. Based on these Orlicz-amalgam spaces, the authors introduce a new kind of Hardy type spaces, namely martingale Hardy–Orlicz-amalgam spaces, which generalize the martingale Hardy-amalgam spaces very recently studied by Bansah and Sehba. Their characterizations via the atomic decompositions are also obtained. As applications of these characterizations, the authors construct the dual theorems in the new framework. Furthermore, the authors also present the boundedness of fractional integral operators <span>(I_alpha )</span> on martingale Hardy–Orlicz-amalgam spaces.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587232","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":"Characterization of a-Birkhoff–James orthogonality in (C^*)-algebras and its applications","authors":"Hooriye Sadat Jalali Ghamsari,&nbsp;Mahdi Dehghani","doi":"10.1007/s43034-024-00339-8","DOIUrl":"10.1007/s43034-024-00339-8","url":null,"abstract":"<div><p>Let <span>({mathcal {A}})</span> be a unital <span>(C^*)</span>-algebra with unit <span>(1_{{mathcal {A}}})</span> and let <span>(ain {mathcal {A}})</span> be a positive and invertible element. Suppose that <span>({mathcal {S}}({mathcal {A}}))</span> is the set of all states on <span>(mathcal {{mathcal {A}}})</span> and let </p><div><div><span>$$begin{aligned} {mathcal {S}}_a ({mathcal {A}})=left{ dfrac{f}{f(a)} , : , f in {mathcal {S}}({mathcal {A}}), , f(a)ne 0right} . end{aligned}$$</span></div></div><p>The norm <span>( Vert xVert _a )</span> for every <span>( x in {mathcal {A}} )</span> is defined by </p><div><div><span>$$begin{aligned} Vert xVert _a = sup _{varphi in {mathcal {S}}_a ({mathcal {A}}) } sqrt{varphi (x^* ax)}. end{aligned}$$</span></div></div><p>In this paper, we aim to investigate the notion of Birkhoff–James orthogonality with respect to the norm <span>(Vert cdot Vert _a)</span> in <span>({mathcal {A}},)</span> namely <i>a</i>-Birkhoff–James orthogonality. The characterization of <i>a</i>-Birkhoff–James orthogonality in <span>({mathcal {A}})</span> by means of the elements of generalized state space <span>({mathcal {S}}_a({mathcal {A}}))</span> is provided. As an application, a characterization for the best approximation to elements of <span>({mathcal {A}})</span> in a subspace <span>({mathcal {B}})</span> with respect to <span>(Vert cdot Vert _a)</span> is obtained. Moreover, a formula for the distance of an element of <span>({mathcal {A}})</span> to the subspace <span>({mathcal {B}}={mathbb {C}}1_{{mathcal {A}}})</span> is given. We also study the strong version of <i>a</i>-Birkhoff–James orthogonality in <span>( {mathcal {A}} .)</span> The classes of <span>(C^*)</span>-algebras in which these two types orthogonality relationships coincide are described. In particular, we prove that the condition of the equivalence between the strong <i>a</i>-Birkhoff–James orthogonality and <span>({mathcal {A}})</span>-valued inner product orthogonality in <span>({mathcal {A}})</span> implies that the center of <span>({mathcal {A}})</span> is trivial. Finally, we show that if the (strong) <i>a</i>-Birkhoff–James orthogonality is right-additive (left-additive) in <span>({mathcal {A}},)</span> then the center of <span>({mathcal {A}})</span> is trivial.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"15 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586748","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}