发布求助
文献互助 智能选刊 最新文献

arXiv: Functional Analysis最新文献

筛选
英文 中文
Positive operator-valued measures and densely defined operator-valued frames 正算子值测度和密定义算子值框架
arXiv: Functional Analysis Pub Date : 2020-04-24 DOI: 10.1216/RMJ.2021.51.265
B. Robinson, Bill Moran, D. Cochran
{"title":"Positive operator-valued measures and densely defined operator-valued frames","authors":"B. Robinson, Bill Moran, D. Cochran","doi":"10.1216/RMJ.2021.51.265","DOIUrl":"https://doi.org/10.1216/RMJ.2021.51.265","url":null,"abstract":"In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the purpose of computing measurement probabilities. Frames and their most common generalizations can be seen to give rise to POVMs, but does every reasonable POVM arise from a type of frame? In this paper we answer this question using a Radon-Nikodym-type result.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80509956","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
Statistically multiplicative convergence on locally solid Riesz algebras 局部实Riesz代数上的统计乘法收敛性
arXiv: Functional Analysis Pub Date : 2020-04-23 DOI: 10.3906/mat-2102-20
A. Aydın, M. Et
{"title":"Statistically multiplicative convergence on locally solid Riesz algebras","authors":"A. Aydın, M. Et","doi":"10.3906/mat-2102-20","DOIUrl":"https://doi.org/10.3906/mat-2102-20","url":null,"abstract":"In this paper, we introduce the statistically multiplicative convergent sequences in locally solid Riesz algebras with respect to the algebra multiplication and the solid topology. We study on this concept and we give the notion of $mathbb{st_m}$-bounded sequence, and also, we prove some relations between this convergence and the other convergences such as the order convergence and the statistical convergence in topological spaces. Also, we give some results related to semiprime $f$-algebras.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83872801","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 existence of fixed points for typical nonexpansive mappings on spaces with positive curvature 正曲率空间上典型非扩张映射不动点的存在性
arXiv: Functional Analysis Pub Date : 2020-04-06 DOI: 10.12775/TMNA.2020.040
C. Bargetz, Michael Dymond, Emir Medjic, S. Reich
{"title":"On the existence of fixed points for typical nonexpansive mappings on spaces with positive curvature","authors":"C. Bargetz, Michael Dymond, Emir Medjic, S. Reich","doi":"10.12775/TMNA.2020.040","DOIUrl":"https://doi.org/10.12775/TMNA.2020.040","url":null,"abstract":"We show that the typical nonexpansive mapping on a small enough subset of a CAT($kappa$)-space is a contraction in the sense of Rakotch. By typical we mean that the set of nonexpansive mapppings without this property is a $sigma$-porous set and therefore also of the first Baire category. Moreover, we exhibit metric spaces where strict contractions are not dense in the space of nonexpansive mappings. In some of these cases we show that all continuous self-mappings have a fixed point nevertheless.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75438608","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 spectrum of the restriction to an invariant subspace 对不变子空间的限制的谱
arXiv: Functional Analysis Pub Date : 2020-04-01 DOI: 10.7153/oam-2020-14-19
D. Drivaliaris, N. Yannakakis
{"title":"The spectrum of the restriction to an invariant subspace","authors":"D. Drivaliaris, N. Yannakakis","doi":"10.7153/oam-2020-14-19","DOIUrl":"https://doi.org/10.7153/oam-2020-14-19","url":null,"abstract":"Let $X$ be a Banach space, $Ain B(X)$ and $M$ be an invariant subspace of $A$. We present an alternative proof that, if the spectrum of the restriction of $A$ to $M$ contains a point that is in any given hole in the spectrum of $A$, then the entire hole is in the spectrum of the restriction.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74011430","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: 2
A note on approximation of continuous functions on normed spaces 赋范空间上连续函数的逼近问题
arXiv: Functional Analysis Pub Date : 2020-04-01 DOI: 10.15330/cmp.12.1.107-110
M. A. Mytrofanov, A. Ravsky
{"title":"A note on approximation of continuous functions on normed spaces","authors":"M. A. Mytrofanov, A. Ravsky","doi":"10.15330/cmp.12.1.107-110","DOIUrl":"https://doi.org/10.15330/cmp.12.1.107-110","url":null,"abstract":"Let $X$ be a real separable normed space $X$ admitting a separating polynomial. We prove that each continuous function from a subset $A$ of $X$ to a real Banach space can be uniformly approximated by restrictions to $A$ of functions which are analytic on open subsets of $X$. Also we prove that each continuous function to a complex Banach space from a complex separable normed space admitting a separating $*$-polynomial can be uniformly approximated by $*$-analytic functions.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85229069","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
Interpolation and duality in algebras of multipliers on the ball 球上乘数代数的插值和对偶性
arXiv: Functional Analysis Pub Date : 2020-03-31 DOI: 10.4171/jems/1245
K. Davidson, Michael Hartz
{"title":"Interpolation and duality in algebras of multipliers on the ball","authors":"K. Davidson, Michael Hartz","doi":"10.4171/jems/1245","DOIUrl":"https://doi.org/10.4171/jems/1245","url":null,"abstract":"We study the multiplier algebras $A(mathcal{H})$ obtained as the closure of the polynomials on certain reproducing kernel Hilbert spaces $mathcal{H}$ on the ball $mathbb{B}_d$ of $mathbb{C}^d$. Our results apply, in particular, to the Drury-Arveson space, the Dirichlet space and the Hardy space on the ball. We first obtain a complete description of the dual and second dual spaces of $A(mathcal H)$ in terms of the complementary bands of Henkin and totally singular measures for $operatorname{Mult}(mathcal{H})$. This is applied to obtain several definitive results in interpolation. In particular, we establish a sharp peak interpolation result for compact $operatorname{Mult}(mathcal{H})$-totally null sets as well as a Pick and peak interpolation theorem. Conversely, we show that a mere interpolation set is $operatorname{Mult}(mathcal{H})$-totally null.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76882106","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 dense subsets of matrices with distinct eigenvalues and distinct singular values 具有不同特征值和不同奇异值的矩阵的密集子集
arXiv: Functional Analysis Pub Date : 2020-03-29 DOI: 10.13001/ela.2020.5329
Himadri Lal Das, M. Kannan
{"title":"On the dense subsets of matrices with distinct eigenvalues and distinct singular values","authors":"Himadri Lal Das, M. Kannan","doi":"10.13001/ela.2020.5329","DOIUrl":"https://doi.org/10.13001/ela.2020.5329","url":null,"abstract":"It is well known that the set of all $ n times n $ matrices with distinct eigenvalues is a dense subset of the set of all real or complex $ n times n $ matrices. In [Hartfiel, D. J. Dense sets of diagonalizable matrices. Proc. Amer. Math. Soc., 123(6): 1669-1672, 1995.], the author established a necessary and sufficient condition for a subspace of the set of all $n times n$ matrices to have a dense subset of matrices with distinct eigenvalues. We are interested in finding a few necessary and sufficient conditions for a subset of the set of all $n times n$ real or complex matrices to have a dense subset of matrices with distinct eigenvalues. Some of our results are generalizing the results of Hartfiel. Also, we study the existence of dense subsets of matrices with distinct singular values, distinct analytic eigenvalues, and distinct analytic singular values, respectively, in the subsets of the set of all real or complex matrices.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84973630","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
A new treatment of convex functions 凸函数的一种新处理
arXiv: Functional Analysis Pub Date : 2020-03-24 DOI: 10.22541/AU.159991025.58949527
M. Sababheh, Shigeru Furuichi, H. Moradi
{"title":"A new treatment of convex functions","authors":"M. Sababheh, Shigeru Furuichi, H. Moradi","doi":"10.22541/AU.159991025.58949527","DOIUrl":"https://doi.org/10.22541/AU.159991025.58949527","url":null,"abstract":"Convex functions have played a major role in the field of Mathematical inequalities. In this paper, we introduce a new concept related to convexity, which proves better estimates when the function is somehow more convex than another. In particular, we define what we called $g-$convexity as a generalization of $log-$convexity. Then we prove that $g-$convex functions have better estimates in certain known inequalities like the Hermite-Hadard inequality, super additivity of convex functions, the Majorization inequality and some means inequalities. Strongly related to this, we define the index of convexity as a measure of ``how much the function is convex\". \u0000Applications including Hilbert space operators, matrices and entropies will be presented in the end.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89658028","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
Invertibility Issues for Toeplitz Plus Hankel Operators and Their Close Relatives Toeplitz + Hankel算子及其近亲的可逆性问题
arXiv: Functional Analysis Pub Date : 2020-03-20 DOI: 10.1007/978-3-030-51945-2_7
V. Didenko, B. Silbermann
{"title":"Invertibility Issues for Toeplitz Plus Hankel Operators and Their Close Relatives","authors":"V. Didenko, B. Silbermann","doi":"10.1007/978-3-030-51945-2_7","DOIUrl":"https://doi.org/10.1007/978-3-030-51945-2_7","url":null,"abstract":"","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88302385","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: 2
On compact subsets of Sobolev spaces on manifolds 流形上Sobolev空间的紧子集
arXiv: Functional Analysis Pub Date : 2020-03-13 DOI: 10.1090/tran/8322
L. Skrzypczak, C. Tintarev
{"title":"On compact subsets of Sobolev spaces on manifolds","authors":"L. Skrzypczak, C. Tintarev","doi":"10.1090/tran/8322","DOIUrl":"https://doi.org/10.1090/tran/8322","url":null,"abstract":"It is common that a Sobolev space defined on $mathbb{R}^m$ has a non-compact embedding into an $L^p$-space, but it has subspaces for which this embedding becomes compact. There are three well known cases of such subspaces, the Rellich compactness, for a subspace of functions on a bounded domain (or an unbounded domain, sufficiently thin at infinity), the Strauss compactness, for a subspace of radially symmetric functions in $mathbb{R}^m$, and the weighted Sobolev spaces. Known generalizations of Strauss compactness include subspaces of functions with block-radial symmetry, subspaces of functions with certain symmetries on Riemannian manifolds, as well as similar subspaces of more general Besov and Triebel-Lizorkin spaces. Presence of symmetries can be interpreted in terms of the rising critical Sobolev exponent corresponding to the smaller effective dimension of the quotient space.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84486046","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信