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Pointwise lineability in sequence spaces 序列空间中的点线性性
arXiv: Functional Analysis Pub Date : 2020-11-02 DOI: 10.1016/j.indag.2020.12.006
D. Pellegrino, A. Raposo
{"title":"Pointwise lineability in sequence spaces","authors":"D. Pellegrino, A. Raposo","doi":"10.1016/j.indag.2020.12.006","DOIUrl":"https://doi.org/10.1016/j.indag.2020.12.006","url":null,"abstract":"","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":"69 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73473630","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: 7
On the geometry of Banach spaces of the form 𝐿𝑖𝑝₀(𝐶(𝐾)) 关于形式为𝐿￣𝑝₀(𝐾(𝐾))的Banach空间的几何
arXiv: Functional Analysis Pub Date : 2020-10-25 DOI: 10.1090/proc/15420
Leandro Candido, P. Kaufmann
{"title":"On the geometry of Banach spaces of the form 𝐿𝑖𝑝₀(𝐶(𝐾))","authors":"Leandro Candido, P. Kaufmann","doi":"10.1090/proc/15420","DOIUrl":"https://doi.org/10.1090/proc/15420","url":null,"abstract":"We investigate the problem of classifying the Banach spaces $mathrm{Lip}_0(C(K))$ for Hausdorff compacta $K$. In particular, sufficient conditions are established for a space $mathrm{Lip}_0(C(K))$ to be isomorphic to $mathrm{Lip}_0(c_0(varGamma))$ for some uncountable set $varGamma$.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77266889","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: 4
Homomorphisms of Fourier–Stieltjes algebras Fourier-Stieltjes代数的同态
arXiv: Functional Analysis Pub Date : 2020-10-13 DOI: 10.4064/sm200206-6-8
Ross Stokke
{"title":"Homomorphisms of Fourier–Stieltjes algebras","authors":"Ross Stokke","doi":"10.4064/sm200206-6-8","DOIUrl":"https://doi.org/10.4064/sm200206-6-8","url":null,"abstract":"Every homomorphism $varphi: B(G) rightarrow B(H)$ between Fourier-Stieltjes algebras on locally compact groups $G$ and $H$ is determined by a continuous mapping $alpha: Y rightarrow Delta(B(G))$, where $Y$ is a set in the open coset ring of $H$ and $Delta(B(G))$ is the Gelfand spectrum of $B(G)$ (a $*$-semigroup). We exhibit a large collection of maps $alpha$ for which $varphi=j_alpha: B(G) rightarrow B(H)$ is a completely positive/completely contractive/completely bounded homomorphism and establish converse statements in several instances. For example, we fully characterize all completely positive/completely contractive/completely bounded homomorphisms $varphi: B(G) rightarrow B(H)$ when $G$ is a Euclidean- or $p$-adic-motion group. In these cases, our description of the completely positive/completely contractive homomorphisms employs the notion of a \"fusion map of a compatible system of homomorphisms/affine maps\" and is quite different from the Fourier algebra situation.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":"46 1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83387666","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
The Truncated Moment Problem for Unital Commutative R-Algebras 一元可交换r -代数的截断矩问题
arXiv: Functional Analysis Pub Date : 2020-09-10 DOI: 10.7900/jot.2021nov26.2392
R. Curto, M. Ghasemi, M. Infusino, S. Kuhlmann
{"title":"The Truncated Moment Problem for Unital Commutative R-Algebras","authors":"R. Curto, M. Ghasemi, M. Infusino, S. Kuhlmann","doi":"10.7900/jot.2021nov26.2392","DOIUrl":"https://doi.org/10.7900/jot.2021nov26.2392","url":null,"abstract":"Let A be a unital commutative R-algebra, B a linear subspace of A and K a closed subset of the character space of A. For a linear functional L: B --> R, we investigate conditions under which L admits an integral representation with respect to a positive Radon measure supported in K. When A is equipped with a submultiplicative seminorm, we employ techniques from the theory of positive extensions of linear functionals to prove a criterion for the existence of such an integral representation for L. When no topology is prescribed on A, we identify suitable assumptions on B, A, L and K which allow us to construct a seminormed structure on A, so as to exploit our previous result to get an integral representation for L. We then use our main theorems to obtain, as applications, several well known results on the classical truncated moment problem, the moment problem for point processes, and the subnormal completion problem for 2-variable weighted shifts.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80059242","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: 6
On tensor fractions and tensor products in the category of stereotype spaces 关于原型空间范畴中的张量分数和张量积
arXiv: Functional Analysis Pub Date : 2020-09-07 DOI: 10.1070/SM9508
S. Akbarov
{"title":"On tensor fractions and tensor products in the category of stereotype spaces","authors":"S. Akbarov","doi":"10.1070/SM9508","DOIUrl":"https://doi.org/10.1070/SM9508","url":null,"abstract":"We prove two identities that connect some natural tensor products in the category $sf{LCS}$ of locally convex spaces with the tensor products in the category $sf{Ste}$ of stereotype spaces. In particular, we give sufficient conditions under which the identity $$ X^vartriangleodot Y^vartrianglecong (X^vartrianglecdot Y^vartriangle)^vartrianglecong (Xcdot Y)^vartriangle $$ holds, where $odot$ is the injective tensor product in the category $sf{Ste}$, $cdot$, the primary tensor product in the category $sf{LCS}$, and $vartriangle$, the pseudosaturation operation in the category $sf{LCS}$. Studying the relations of this type is justified by the fact that they turn out to be important instruments for constructing duality theory based on the notion of envelope. In particular, they are used in the construction of the duality theory for the class of (not necessarily, Abelian) countable discrete groups.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80021649","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: 1
On generalized {Phi}-strongly monotone mappings and algorithms for the solution of equations of Hammerstein type 关于广义{Phi}-强单调映射和Hammerstein型方程解的算法
arXiv: Functional Analysis Pub Date : 2020-08-18 DOI: 10.22075/ijnaa.2019.16797.1894
M. Aibinu, O. Mewomo
{"title":"On generalized {Phi}-strongly monotone mappings and algorithms for the solution of equations of Hammerstein type","authors":"M. Aibinu, O. Mewomo","doi":"10.22075/ijnaa.2019.16797.1894","DOIUrl":"https://doi.org/10.22075/ijnaa.2019.16797.1894","url":null,"abstract":"In this paper, we consider the class of generalized {Phi}-strongly monotone mappings and the methods of approximating a solution of equations of Hammerstein type. Auxiliary mapping is defined for nonlinear integral equations of Hammerstein type. The auxiliary mapping is the composition of bounded generalized {Phi}-strongly monotone mappings which satisfy the range condition. Suitable conditions are imposed to obtain the boundedness and to show that the auxiliary mapping is a generalized {Phi}-strongly which satisfies the range condition. A sequence is constructed and it is shown that it converges strongly to a solution of equations of Hammerstein type. The results in this paper improve and extend some recent corresponding results on the approximation of a solution of equations of Hammerstein type.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86229915","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
Strong convergence theorems for strongly monotone mappings in Banach spaces Banach空间中强单调映射的强收敛定理
arXiv: Functional Analysis Pub Date : 2020-08-18 DOI: 10.5269/bspm.37655
M. Aibinu, O. Mewomo
{"title":"Strong convergence theorems for strongly monotone mappings in Banach spaces","authors":"M. Aibinu, O. Mewomo","doi":"10.5269/bspm.37655","DOIUrl":"https://doi.org/10.5269/bspm.37655","url":null,"abstract":"Let $E$ be a uniformly smooth and uniformly convex real Banach space and $E^*$ be its dual space. Suppose $A : Erightarrow E^*$ is bounded, strongly monotone and satisfies the range condition such that $A^{-1}(0)neq emptyset$. Inspired by Alber [2], we introduce Lyapunov functions and use the new geometric properties of Banach spaces to show the strong convergence of an iterative algorithm to the solution of $Ax=0$.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74631731","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: 4
The diametral strong diameter 2 property of Banach spaces is the same as the Daugavet property Banach空间的直径强直径2性质与道格韦性质相同
arXiv: Functional Analysis Pub Date : 2020-08-17 DOI: 10.1090/proc/15448
V. Kadets
{"title":"The diametral strong diameter 2 property of Banach spaces is the same as the Daugavet property","authors":"V. Kadets","doi":"10.1090/proc/15448","DOIUrl":"https://doi.org/10.1090/proc/15448","url":null,"abstract":"We demonstrate the result stated in the title, thus answering an open question asked by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda Zoca in J. Conv. Anal. textbf{25}, no. 3 (2018).","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":"541 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78997816","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: 10
Ball proximinality of $M$-ideals of compact operators 紧算子M -理想的球邻近性
arXiv: Functional Analysis Pub Date : 2020-08-15 DOI: 10.1090/PROC/15446
C. R. Jayanarayanan, Sreejith Siju
{"title":"Ball proximinality of $M$-ideals of compact operators","authors":"C. R. Jayanarayanan, Sreejith Siju","doi":"10.1090/PROC/15446","DOIUrl":"https://doi.org/10.1090/PROC/15446","url":null,"abstract":"In this article, we prove the proximinality of closed unit ball of $M$-ideals of compact operators. We also prove the ball proximinality of $M$-embedded spaces in their biduals. Moreover, we show that $mathcal{K}(ell_1)$, the space of compact operators on $ell_1$, is ball proximinal in $mathcal{B}(ell_1)$, the space of bounded operators on $ell_1$, even though $mathcal{K}(ell_1)$ is not an $M$-ideal in $mathcal{B}(ell_1)$.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85172824","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
Subnormal nth roots of quasinormal operators are quasinormal 拟正规算子的次正规n根是拟正规的
arXiv: Functional Analysis Pub Date : 2020-08-08 DOI: 10.1016/J.JFA.2021.109001
Paweł Pietrzycki
{"title":"Subnormal nth roots of quasinormal operators are quasinormal","authors":"Paweł Pietrzycki","doi":"10.1016/J.JFA.2021.109001","DOIUrl":"https://doi.org/10.1016/J.JFA.2021.109001","url":null,"abstract":"","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78142291","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: 7
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