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Weakly Compact Sets and Riesz Representation Theorem in Musielak Sequence spaces

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Acta Mathematica Sinica,English Series 2024年第2期40卷 467-484页

作者： Wan Zhong GONG Si Yu SHI Zhong Rui SHI Department of Mathematics Anhui Normal UniversityWuhu 241000P.R.China Smeal College of Business Pennsylvania State UniversityUniversity ParkPennsylwania 16802USA Department of Mathematics Shanghai UniversityShanghai 200444P.R.China

In this work,we give some criteria of the weakly compact sets and a representation theorem of Riesz's type in Musielak sequence spaces using the ideas and techniques of sequence spaces and Musielak ***,as an immediate consequence of the criteria considered in this paper,the criteria of the weakly compact sets of Orlicz sequence spaces are deduced.

关键词： Compact set weak topology Banach space dual space Musielak sequence spaces

Norming Subspaces Isomorphic to l_1

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Acta Mathematica Sinica,English Series 2015年第5期31卷 767-771页

作者： Sofiya OSTROVSKA Department of Mathematics Atilim University

Norming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators. The main result of this article asserts that the dual of a Banach space X contains a norming subspace isomorphic to l1 provided that the following two conditions are satisfied：（1） X＊ contains a subspace isomorphic to l1; and （2） X＊ contains a separable norming subspace.

关键词： Banach space norming subspace dual space weak* convergence free ultrafilter

Hardy-Sobolev spaces and their multipliers

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Science China Mathematics 2014年第11期57卷 2361-2368页

作者： CAO GuangFu HE Li Department of Mathematics Guangzhou University Department of Mathematics Sun Yat-sen University

In this paper,some properties of Hardy-Sobolev spaces are obtained. The multipliers on these spaces are defined,and our results show that the multiplier algebra is more complex than that on the classical Hardy spaces.... 详细信息

关键词： Hardy-Sobolev space dual space spectrum

Modules　over　Operator　Algebras　and　Its　Module　Maps

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Communications in Mathematical Research 1997年第1期 109-116页

作者：许天周

ＭｏｄｕｌｅｓｏｖｅｒＯｐｅｒａｔｏｒＡｌｇｅｂｒａｓａｎｄＩｔｓＭｏｄｕｌｅＭａｐｓＸｕＴｉａｎｚｈｏｕ（许天周）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＵｎｉｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ，... 详细信息

ＭｏｄｕｌｅｓｏｖｅｒＯｐｅｒａｔｏｒＡｌｇｅｂｒａｓａｎｄＩｔｓＭｏｄｕｌｅＭａｐｓＸｕＴｉａｎｚｈｏｕ（许天周）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＵｎｉｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ，２１００９３）ＡｂｓｔｒａｃｔＬｅ...

关键词： and Phrases Banach Module Module Map Locally Convex Topological space dual space Operator Algebra.

ON SIMULTANEOUS WEAKLY-CHEBYSHEV SUBspaceS

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Analysis in Theory and Applications 2011年第2期27卷 117-124页

作者： Sh. Rezapour H. Alizadeh S. M. Vaezpour Azarbaidjan University of Tarbiat Moallem Aazad Islamic University Amirkabir University of Technology

In this paper, we shall introduce and characterize simultaneous quasi-Chebyshev （and weakly-Chebyshev） subspaces of normed spaces with respect to a bounded set S by using elements of the dual space.

关键词： dual space best simultaneous approximation simultaneous quasi-Chebyshevsubspace simultaneous weakly-Chebyshev subspace

Classical Fourier Analysis over Homogeneous spaces of Compact Groups

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Analysis in Theory and Applications 2016年第4期32卷 339-354页

作者： Arash Ghaani Farashahi Numerical Harmonic Analysis Group (NuHAG) Faculty Mathematics University of Vienna

This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 （G / H, μ）.

关键词： Compact group homogeneous space dual space Fourier transform Plancherel(trace) formula Peter-Weyl Theorem

Fock-Sobolev spaces and Weighted Composition Operators among Them

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Communications in Mathematical Research 2016年第4期32卷 303-318页

作者： he li cao guang-fu ji you-qing School of Mathematics Guangzhou UniversityGuangzhou510006 不详

Abstract： We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss ... 详细信息

关键词： Fock-Sobolev space dual space weighted composition operator

Axioms in the Variety of eO-Algebras

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Journal of Mathematical Research and Exposition 2008年第3期28卷 699-705页

作者： FANG Jie SUN Zhong Ju Department of Mathematics Shantou University Guangdong 515063 China Faculty of Mathematics and Computer Science Guangdong Polytechnic Normal University Guangdong 510665 China

The variety eO of extended Ockham algebras consists of those algebras （L; ∧, ∨, f, k, 0, 1） such that （L; ∧, ∨, 0, 1） is a bounded distributive lattice together with a dual endomorphism f on L and an endomorphism k on L such that fk = kf. In this paper we extend Urquhart＇s theorem to eO-algebras and we are in particular concerned with the subclass e2M of eO-algebras in which f^2 = id and k^2 = id. We show that there are 19 non-equivalent axioms in e2M and then order them by implication.

关键词： Extended Ockham algebra dual space subdirectly irreducible algebra equational basis.

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保一秩投影算子定理的一个简单证明及其推广

陕西师大学报(自然科学版) 1988年第2期 90-91页

作者：冯文英陕西师大数学系

设 X 为复的 Banach 空间,L（X）为 X 上的有界线性算子构成的 Banach 代数,F为L（X）到L（X）的线性算子.Matj（?）z Omladi（?）在[1]中证明了下面的定理.定理设 F:L（X）→L（X）是线性、双射且在弱算子拓扑下连续的映射,F 和 F-1均... 详细信息

设 X 为复的 Banach 空间,L（X）为 X 上的有界线性算子构成的 Banach 代数,F为L（X）到L（X）的线性算子.Matj（?）z Omladi（?）在[1]中证明了下面的定理.定理设 F:L（X）→L（X）是线性、双射且在弱算子拓扑下连续的映射,F 和 F-1均保持一秩投影,则或者（1）存在一个有界的双射线性算子 U:X→X,使 F（A）=UAU-1,或者（2）存在一个有界的双射线性算子 U:X′→X,使 F（A）=UA′U-1,在此情形下 X 是自反的.下面给出此定理的一个简单证明,并对其条件进行改善,推广该定理.本文中 X、Y 表示 Banach 空间,X′、Y′分别表示它们的对偶空间,任意 x∈X,f∈X′,x（?）f 表示如下定义的 X 上的一秩算子,任意 y∈x,（x（?）f）（3y）=f（y）x.以下两个引理均设 F 为 L（X）到 L（Y）的保持一秩投影的线性映射,且 F 限制在 L（X）中的一秩算子组成的集合上为单射.引理1 若 x、y∈X 为线性无关向量,f∈X′为非零函数且 f（x）=f（y）=1,则存在 u、

关键词： projection of rank 1 dual space