Annals of Functional Analysis最新文献

{"title":"Variations of the James and Schäffer constants in Banach spaces","authors":"Horst Martini,&nbsp;Pier Luigi Papini,&nbsp;Senlin Wu","doi":"10.1007/s43034-023-00308-7","DOIUrl":"10.1007/s43034-023-00308-7","url":null,"abstract":"<div><p>We study two constants <span>(g_1(X))</span> and <span>(J_1(X))</span> introduced by Fu et al. (Symmetry 13(6):951, 2021), present new characterizations of them, clarify detailed relations of these constants to James and Schäffer constants as well as the relation between <span>(J_1(X))</span> and <span>(A_2(X))</span> defined by Baronti et al. (J Math Anal Appl 252(1):124–146, 2000). We also pose several problems.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138502206","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 pseudo-regularity of the range of orthogonal projections in Krein spaces","authors":"Lulu Zhang,&nbsp;Guojun Hai","doi":"10.1007/s43034-023-00307-8","DOIUrl":"10.1007/s43034-023-00307-8","url":null,"abstract":"<div><p>Let <i>P</i>, <i>Q</i> be two orthogonal projections and <i>J</i> be a symmetry such that <span>(JP=QJ)</span>. Based on the block operator technique and Halmos’ CS decomposition, we devote to characterizing the pseudo-regularity of <span>({mathcal {R}}(P))</span> and <span>({mathcal {R}}(Q))</span>. It is given the <i>J</i>-projection onto a regular complement of <span>({mathcal {R}}(P)^{circ })</span> in <span>({mathcal {R}}(P))</span> (resp. <span>({mathcal {R}}(Q)^{circ })</span> in <span>({mathcal {R}}(Q))</span>). Furthermore, the sets of <i>J</i>-normal projections onto <span>({mathcal {R}}(P))</span> and <span>({mathcal {R}}(Q))</span> are obtained.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138438395","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":"Positive periodic solutions for certain kinds of delayed q-difference equations with biological background","authors":"Marko Kostić,&nbsp;Halis Can Koyuncuoğlu,&nbsp;Youssef N. Raffoul","doi":"10.1007/s43034-023-00306-9","DOIUrl":"10.1007/s43034-023-00306-9","url":null,"abstract":"<div><p>This paper specifically focuses on a specific type of <i>q</i>-difference equations that incorporate multiple delays. The main objective is to explore the existence of positive periodic solutions using coincidence degree theory. Notably, the equation studied in this paper has relevance to important biological growth models constructed on quantum domains. The significance of this research lies in the fact that quantum domains are not translation invariant. By investigating periodic solutions on quantum domains, the paper introduces a new perspective and makes notable advancements in the related literature, which predominantly focuses on translation invariant domains. This research contributes to a better understanding of periodic dynamics in systems governed by <i>q</i>-difference equations with multiple delays, particularly in the context of biological growth models on quantum domains.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796629","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":"Genuine Bernstein–Durrmeyer type operators preserving 1 and (x^j)","authors":"Ulrich Abel,&nbsp;Ana Maria Acu,&nbsp;Margareta Heilmann,&nbsp;Ioan Raşa","doi":"10.1007/s43034-023-00305-w","DOIUrl":"10.1007/s43034-023-00305-w","url":null,"abstract":"<div><p>We introduce a family of genuine Bernstein–Durrmeyer type operators preserving the functions 1 and <span>(x^j)</span>. For them, we establish Voronovskaja type formulas. The behaviour with respect to generalized convex functions is investigated.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797713","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":"Fixed Point Theorem: variants, affine context and some consequences","authors":"Anderson L. A. de Araujo,&nbsp;Edir J. F. Leite","doi":"10.1007/s43034-023-00304-x","DOIUrl":"10.1007/s43034-023-00304-x","url":null,"abstract":"<div><p>In this work, we will present variants Fixed Point Theorem for the affine and classical contexts, as a consequence of general Brouwer’s Fixed Point Theorem. For instance, the affine results will allow working on affine balls, which are defined through the affine <span>(L^{p})</span> functional <span>(mathcal {E}_{p,Omega }^p)</span> introduced by Lutwak et al. (J Differ Geom 62:17–38, 2002) for <span>(p &gt; 1)</span> that is non convex and does not represent a norm in <span>(mathbb {R}^m)</span>. Moreover, we address results for discontinuous functional at a point. As an application, we study critical points of the sequence of affine functionals <span>(Phi _m)</span> on a subspace <span>(W_m)</span> of dimension <i>m</i> given by </p><div><div><span>$$begin{aligned} Phi _m(u)=frac{1}{p}mathcal {E}_{p, Omega }^{p}(u) - frac{1}{alpha }Vert uVert ^{alpha }_{L^alpha (Omega )}- int _{Omega }f(x)u textrm{d}x, end{aligned}$$</span></div></div><p>where <span>(1&lt;alpha &lt;p)</span>, <span>([W_m]_{m in mathbb {N}})</span> is dense in <span>(W^{1,p}_0(Omega ))</span> and <span>(fin L^{p'}(Omega ))</span>, with <span>(frac{1}{p}+frac{1}{p'}=1)</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-023-00304-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50511163","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":"Some properties of the extremal function for the Fuglede p-modulus","authors":"Małgorzata Ciska-Niedziałomska","doi":"10.1007/s43034-023-00303-y","DOIUrl":"10.1007/s43034-023-00303-y","url":null,"abstract":"<div><p>We deal with the Fuglede <i>p</i>-modulus of a system of measures, focusing on three aspects. First, we combine results concerning Badger’s criterion for the extremal function, i.e., the function which realizes the <i>p</i>-modulus, and plans with barycenter in <span>(L^q)</span>, which give an alternative—in a sense, probabilistic—approach to <i>p</i>-modulus. It seems that the correlation of these results has not yet been established. Second, we deal with families of measures for which the integral of the extremal function is one. On such a family, the <i>p</i>-modulus as well as the optimal plans are concentrated. We consider closures of these families and relate them with generic families of measures for which the extremal function exists. Finally, we compute the <i>p</i>-modulus and extremal function for finite families of measures.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-023-00303-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50511164","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":"Estimates for bilinear generalized fractional integral operator and its commutator on generalized Morrey spaces over RD-spaces","authors":"Guanghui Lu,&nbsp;Shuangping Tao,&nbsp;Miaomiao Wang","doi":"10.1007/s43034-023-00302-z","DOIUrl":"10.1007/s43034-023-00302-z","url":null,"abstract":"<div><p>Let <span>((X,d,mu ))</span> be an RD-space. In this paper, we prove that a bilinear generalized fractional integral <span>(widetilde{T}_{alpha })</span> is bounded from the product of generalized Morrey spaces <span>(mathcal {L}^{varphi _{1},p_{1}}(X)times mathcal {L}^{varphi _{2},p_{2}}(X))</span> into spaces <span>(mathcal {L}^{varphi ,q}(X))</span>, and it is also bounded from the product of spaces <span>(mathcal {L}^{varphi _{1},p_{1}}(X)times mathcal {L}^{varphi _{2},p_{2}}(X))</span> into generalized weak Morrey spaces <span>(Wmathcal {L}^{varphi ,q}(X))</span>, where the Lebesgue measurable functions <span>(varphi _{1}, varphi _{2})</span> and <span>(varphi )</span> satisfy certain conditions and <span>(varphi _{1}varphi _{2}=varphi )</span>, <span>(alpha in (0,1))</span> and <span>(frac{1}{q}=frac{1}{p_{1}}+frac{1}{p_{2}}-2alpha )</span> for <span>(1&lt;p_{1}, p_{2}&lt;frac{1}{alpha })</span>. Furthermore, we establish the boundedness of the commutator <span>(widetilde{T}_{alpha ,b_{1},b_{2}})</span> formed by <span>(b_{1},b_{2}in )</span> <span>(textrm{BMO}(X)(hbox {or }textrm{Lip}_{beta }(X)))</span> and <span>(widetilde{T}_{alpha })</span> on spaces <span>(mathcal {L}^{varphi ,q}(X))</span> and on spaces <span>(Wmathcal {L}^{varphi ,q}(X))</span>. As applications, we show that the <span>(widetilde{T}_{alpha })</span> and its commutator <span>(widetilde{T}_{alpha ,b_{1},b_{2}})</span> are bounded on grand generalized Morrey spaces <span>(mathcal {L}^{theta ,varphi ,p)}(X))</span> over <span>((X,d,mu ))</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50494520","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":"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}