Annals of Functional Analysis最新文献

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

{"title":"The eigenvalues, numerical ranges, and invariant subspaces of the Bergman Toeplitz operators over the bidisk","authors":"Yongning Li,&nbsp;Yin Zhao,&nbsp;Xuanhao Ding","doi":"10.1007/s43034-024-00336-x","DOIUrl":"10.1007/s43034-024-00336-x","url":null,"abstract":"<div><p>In this paper, we consider several questions about the eigenvalues, the numerical ranges, and the invariant subspaces of the Toeplitz operator on the Bergman space over the bidisk and we obtain the corresponding results.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586965","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":"Characterizations for boundedness of fractional maximal function commutators in variable Lebesgue spaces on stratified groups","authors":"Wenjiao Zhao,&nbsp;Jianglong Wu","doi":"10.1007/s43034-024-00334-z","DOIUrl":"10.1007/s43034-024-00334-z","url":null,"abstract":"<div><p>In this paper, the main aim is to consider the mapping properties of the maximal or nonlinear commutator for the fractional maximal operator with the symbols belong to the Lipschitz spaces on variable Lebesgue spaces in the context of stratified Lie groups, with the help of which some new characterizations to the Lipschitz spaces and nonnegative Lipschitz functions are obtained in the stratified groups context. Meanwhile, some equivalent relations between the Lipschitz norm and the variable Lebesgue norm are also given.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586677","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 essential spectrums of (2times 2) unbounded anti-triangular operator matrices","authors":"Xinran Liu,&nbsp;Deyu Wu","doi":"10.1007/s43034-024-00337-w","DOIUrl":"10.1007/s43034-024-00337-w","url":null,"abstract":"<div><p>Let </p><div><div><span>$$begin{aligned} {mathcal {T}}=left( begin{array}{cc} 0 &amp;{}quad B C &amp;{}quad D end{array} right) :D(C)times D(B)subset Xtimes Xrightarrow Xtimes X end{aligned}$$</span></div></div><p>be a <span>(2times 2)</span> unbounded anti-triangular operator matrix on complex Hilbert space <span>(Xtimes X)</span>. Using the relative compact perturbation theory and the space decomposition method, the seven essential spectrum equalities are characterized as </p><div><div><span>$$begin{aligned} sigma _{ei}({mathcal {T}})={lambda in mathbb C:lambda ^2in sigma _{ei}(BC)cup sigma _{ei}(CB)},~~~~iin {1,~2,~3,~4,~5,~6,~7}, end{aligned}$$</span></div></div><p>where <span>(sigma _{ei}(cdot ))</span> (<span>(i=1,ldots ,7)</span>) denote the Gustafson essential spectrum, Weidmann essential spectrum, Kato essential spectrum, Wolf essential spectrum, Schechter essential spectrum, essential approximation point spectrum, and essential defect spectrum, respectively. An example is also provided to illustrate the validity of the criterion.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140358241","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":"Harmonic Bloch space on the real hyperbolic ball","authors":"A. Ersin Üreyen","doi":"10.1007/s43034-024-00335-y","DOIUrl":"10.1007/s43034-024-00335-y","url":null,"abstract":"<div><p>We study the Bloch and the little Bloch spaces of harmonic functions on the real hyperbolic ball. We show that the Bergman projections from <span>(L^infty ({mathbb {B}}))</span> to <span>({mathcal {B}})</span>, and from <span>(C_0({mathbb {B}}))</span> to <span>({mathcal {B}}_0)</span> are onto. We verify that the dual space of the hyperbolic harmonic Bergman space <span>({mathcal {B}}^1_alpha )</span> is <span>({mathcal {B}})</span> and its predual is <span>({mathcal {B}}_0)</span>. Finally, we obtain atomic decompositions of Bloch functions as series of Bergman reproducing kernels.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00335-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140313702","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":"The local Borg–Marchenko uniqueness theorem for Dirac-type systems with locally smooth at the right endpoint rectangular potentials","authors":"Tiezheng Li,&nbsp;Guangsheng Wei","doi":"10.1007/s43034-024-00333-0","DOIUrl":"10.1007/s43034-024-00333-0","url":null,"abstract":"<div><p>We consider self-adjoint Dirac-type systems with rectangular matrix potentials on the interval [0, <i>b</i>),  where <span>(0&lt;ble infty .)</span> We present a new proof of the local Borg–Marchenko uniqueness theorem. The high-energy asymptotics of the Weyl–Titchmarsh functions and the local Borg–Marchenko uniqueness theorem are derived for locally smooth potentials at the right endpoint.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140303201","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}