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Advances in Operator Theory最新文献

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Existence result of bounded variation solution for a perturbed (1-)Laplacian and (1-)biharmonic problem with vanishing potentials 具有消失势的扰动 $$1-$Laplacian 和 $$1-$ 双谐波问题的有界变化解的存在性结果
IF 0.8
Advances in Operator Theory Pub Date : 2024-06-06 DOI: 10.1007/s43036-024-00351-8
Mahsa Amoie, Mohsen Alimohammady
{"title":"Existence result of bounded variation solution for a perturbed (1-)Laplacian and (1-)biharmonic problem with vanishing potentials","authors":"Mahsa Amoie,&nbsp;Mohsen Alimohammady","doi":"10.1007/s43036-024-00351-8","DOIUrl":"10.1007/s43036-024-00351-8","url":null,"abstract":"<div><p>This work focuses on the investigation of a quasilinear elliptic problem in the entire space <span>(mathbb {R}^N)</span>, which involves the 1-Laplacian and 1-biharmonic operators, as well as potentials that can vanish at infinity. This research is conducted within the space of functions with bounded variation. The main result is proven using a version of the mountain pass theorem that does not require the Palais-Smale condition.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141380882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algebraic curves associated with centrosymmetric matrices of orders up to 6 与最高阶数为 6 的中心对称矩阵相关的代数曲线
IF 0.8
Advances in Operator Theory Pub Date : 2024-06-04 DOI: 10.1007/s43036-024-00353-6
N. Bebiano, R. Lemos, G. Soares
{"title":"Algebraic curves associated with centrosymmetric matrices of orders up to 6","authors":"N. Bebiano,&nbsp;R. Lemos,&nbsp;G. Soares","doi":"10.1007/s43036-024-00353-6","DOIUrl":"10.1007/s43036-024-00353-6","url":null,"abstract":"<div><p>In this paper the boundary generating curves and numerical ranges of centrosymmetric matrices of orders up to 6 are characterized in terms of the matrices entries. These results extend previous ones concerning Kac-Sylvester matrices. The classification of all the possible boundary generating curves for centrosymmetric matrices of higher dimensions remains open.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00353-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141267754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some remarks on the mutually commutative idempotents 关于互换幂级数的几点评论
IF 0.8
Advances in Operator Theory Pub Date : 2024-06-03 DOI: 10.1007/s43036-024-00339-4
Wei Luo, Chunhong Fu, Qingxiang Xu
{"title":"Some remarks on the mutually commutative idempotents","authors":"Wei Luo,&nbsp;Chunhong Fu,&nbsp;Qingxiang Xu","doi":"10.1007/s43036-024-00339-4","DOIUrl":"10.1007/s43036-024-00339-4","url":null,"abstract":"<div><p>This paper deals mainly with the idempotency of an operator or a matrix <i>T</i> given by <span>(T=c_1 Pi _1 +c_2 Pi _2+cdots +c_nPi _n,)</span> where <i>n</i> is an arbitrary positive integer, <span>({Pi _{1},Pi _{2},ldots ,Pi _{n}})</span> is a collection of mutually commutative idempotents, and <span>(c_1,c_2,ldots ,c_n)</span> are complex numbers. Some previous results in the cases of <span>(n=2)</span> and <span>(n=3)</span> are generalized, and meanwhile some new characterizations of the idempotency of <i>T</i> are obtained.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141270702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Factorization of two-Lipschitz integral operators 双李普西茨积分算子的因式分解
IF 0.8
Advances in Operator Theory Pub Date : 2024-06-01 DOI: 10.1007/s43036-024-00354-5
Khaled Hamidi
{"title":"Factorization of two-Lipschitz integral operators","authors":"Khaled Hamidi","doi":"10.1007/s43036-024-00354-5","DOIUrl":"10.1007/s43036-024-00354-5","url":null,"abstract":"<div><p>We study the integrability and <i>S</i>-factorizability of two-Lipschitz operators between pointed metric spaces and Banach spaces. We also introduce a factorization theorem and examine its connection with the bi-linearization maps. Finally, we establish a relationship between these two classes of operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141279068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence of solutions to a strongly nonlinear elliptic coupled system of finite order 强非线性有限阶椭圆耦合系统解的存在性
IF 0.8
Advances in Operator Theory Pub Date : 2024-05-29 DOI: 10.1007/s43036-024-00350-9
Manar Lahrache, Mohamed Rhoudaf, Hajar Talbi
{"title":"Existence of solutions to a strongly nonlinear elliptic coupled system of finite order","authors":"Manar Lahrache,&nbsp;Mohamed Rhoudaf,&nbsp;Hajar Talbi","doi":"10.1007/s43036-024-00350-9","DOIUrl":"10.1007/s43036-024-00350-9","url":null,"abstract":"<div><p>The existence of a capacity solution to the strongly nonlinear degenerate problem, namely, <span>(H(theta )+g(x,theta )=sigma (theta )|nabla psi |^{2}, {text {div}}(sigma (theta ) nabla psi )=0)</span> in <span>(Omega )</span> where <span>(g(x,theta ))</span> is a lower order term satisfies the sign condition but without any restriction on its growth and the operator <i>H</i> is of the form </p><div><div><span>$$begin{aligned} H (theta )=sum _{|nu |=0}^{r}(-1)^{|nu |} D^nu left( h_nu left( x, D^gamma theta right) right) , quad |gamma | le |nu |, end{aligned}$$</span></div></div><p>is proved in the framework of Sobolev space of finite order.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Furstenberg fixed point property 关于弗斯滕伯格定点特性
IF 0.8
Advances in Operator Theory Pub Date : 2024-05-29 DOI: 10.1007/s43036-024-00355-4
Khadime Salame
{"title":"On the Furstenberg fixed point property","authors":"Khadime Salame","doi":"10.1007/s43036-024-00355-4","DOIUrl":"10.1007/s43036-024-00355-4","url":null,"abstract":"<div><p>Given an abstract semigroup <i>S</i>, by the Furstenberg fixed point property, we refer to a fixed point property of the following type: Whenever (<i>S</i>, <i>X</i>) is a nonexpansive compact flow with a certain property (P) and nonempty convex phase space <i>X</i> in a Hausdorff locally convex space (<i>E</i>, <i>Q</i>), then there exists a point <span>(xin X)</span> such that <span>(s.x=x)</span> for each <span>(sin S)</span>. Motivated by the Furstenberg’s fixed point theorem on the existence of common fixed points for continuous affine compact flows, we are interested in investigating its natural nonlinear counterpart, and to this end we introduce and study a certain fixed point property for semigroups of nonexpansive mappings.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Numerical solution of eigenvalue problems for a compact integral operator with Green’s kernels 带格林核的紧凑积分算子特征值问题的数值求解
IF 0.8
Advances in Operator Theory Pub Date : 2024-05-25 DOI: 10.1007/s43036-024-00352-7
Hamza Bouda, Chafik Allouch, Zakaria El Allali, Kapil Kant
{"title":"Numerical solution of eigenvalue problems for a compact integral operator with Green’s kernels","authors":"Hamza Bouda,&nbsp;Chafik Allouch,&nbsp;Zakaria El Allali,&nbsp;Kapil Kant","doi":"10.1007/s43036-024-00352-7","DOIUrl":"10.1007/s43036-024-00352-7","url":null,"abstract":"<div><p>This paper presents spectral projection and modified projection methods for approximating the eigenelements of a compact integral operator with <i>Green</i>’s function-type kernels. The projection can either be the orthogonal projection or the interpolatory projection using <i>Legendre</i> polynomials. To the best of our knowledge, this paper is the first to consider the eigenvalue problem with <i>Green</i>’s kernels by global polynomials. We analyze the convergence of these methods and their iterated versions, and we establish superconvergence results. The effectiveness of the proposed approach is illustrated through various numerical tests.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Paths of means for positive operators with strongly unitarily equivalent supports 具有强单位等价支持的正算子的手段路径
IF 0.8
Advances in Operator Theory Pub Date : 2024-05-23 DOI: 10.1007/s43036-024-00344-7
Jun Ichi Fujii
{"title":"Paths of means for positive operators with strongly unitarily equivalent supports","authors":"Jun Ichi Fujii","doi":"10.1007/s43036-024-00344-7","DOIUrl":"10.1007/s43036-024-00344-7","url":null,"abstract":"<div><p>Based on the Bonnabel–Sepulchre geometric mean for fixed rank matrices, we introduced paths of matrix means corresponding to the Kubo–Ando operator ones. We also observed that our mean includes the Batzies–Hüper–Machado–Silva Leite geometric means for fixed rank projection matrices. But these means are restricted to real ones and moreover it seems that it is not easy to extend them to operators on a complex (infinite dimensional) Hilbert space since these means were based on geometries for finite dimensional real spaces. In this paper, we introduce the general paths of means on a complex Hilbert space corresponding to those of the Kubo–Ando ones based on the infinite dimensional complex Grassmann geodesic in the sense of Andruchow.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141107613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New refinements of some classical inequalities via Young’s inequality 通过杨氏不等式对一些经典不等式的新完善
IF 0.8
Advances in Operator Theory Pub Date : 2024-05-18 DOI: 10.1007/s43036-024-00347-4
Mohamed Amine Ighachane, Fuad Kittaneh, Zakaria Taki
{"title":"New refinements of some classical inequalities via Young’s inequality","authors":"Mohamed Amine Ighachane,&nbsp;Fuad Kittaneh,&nbsp;Zakaria Taki","doi":"10.1007/s43036-024-00347-4","DOIUrl":"10.1007/s43036-024-00347-4","url":null,"abstract":"<div><p>The main objective of this paper is to use a new refinement of Young’s inequality to obtain two new scalar inequalities. As an application, we derive several new improvements of some well-known inequalities, which include the generalized mixed Schwarz inequality, numerical radius inequalities, Jensen inequalities and others. For example, for every <span>(T,S in {mathcal {B(H)}})</span>, <span>(alpha in (0,1))</span> and <span>(x, y in {mathcal {H}})</span>, we prove that </p><div><div><span>$$begin{aligned}{} &amp; {} left( 1+ L(alpha )log ^2left( frac{|langle TS x, yrangle | }{r(S)Vert f(|T|) xVert left| gleft( left| T^*right| right) yright| }right) right) |langle TSx, yrangle | {} &amp; {} quad le r(S)Vert f(|T|) xVert left| gleft( left| T^*right| right) yright| , end{aligned}$$</span></div></div><p>where <i>L</i> is a positive 1-periodic function and <i>r</i>(<i>S</i>) is the spectral radius of <i>S</i>, which gives an improvement of the well-known generalized mixed Schwarz inequality: </p><div><div><span>$$begin{aligned} left| langle TSx,y rangle right| le r(S)Vert f(|T|) xVert left| gleft( left| T^*right| right) yright| , end{aligned}$$</span></div></div><p>where <span>(|T| S=S^*|T|)</span> and <i>f</i>, <i>g</i> are non-negative continuous functions defined on <span>([0, infty ))</span> satisfying that <span>(f(t) g(t)=t,(t ge 0))</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141125719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a class of obstacle problem via Young measure in generalized Sobolev space 通过广义索波列夫空间中的杨度量论一类障碍问题
IF 0.8
Advances in Operator Theory Pub Date : 2024-05-17 DOI: 10.1007/s43036-024-00349-2
Mouad Allalou, Mohamed El Ouaarabi, Hasnae El Hammar, Abderrahmane Raji
{"title":"On a class of obstacle problem via Young measure in generalized Sobolev space","authors":"Mouad Allalou,&nbsp;Mohamed El Ouaarabi,&nbsp;Hasnae El Hammar,&nbsp;Abderrahmane Raji","doi":"10.1007/s43036-024-00349-2","DOIUrl":"10.1007/s43036-024-00349-2","url":null,"abstract":"<div><p>This paper deals with the existence and uniqueness of weak solution for a class of obstacle problem of the form </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} &amp;{}displaystyle int _{Omega }mathcal {V}(x,Dw):D(vartheta -w)mathrm {~d}x+displaystyle int _{Omega }leftlangle wvert wvert ^{p(x)-2},vartheta - wrightrangle mathrm {~d}x &amp;{} quad ge displaystyle int _{Omega }mathcal {U}(x,w)(vartheta -w)mathrm {~d}x, ; &amp;{} vartheta in Im _{Lambda , h}, end{array}right. } end{aligned}$$</span></div></div><p>where <span>(Im _{Lambda , h})</span> is a convex set defined below. By using the Young measure theory and Kinderlehrer and Stampacchia Theorem, we prove the existence and uniqueness result of the considered problem in the framework of generalized Sobolev space.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140964265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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