多重调和函数空间的对偶空间

研究了多重调和函数空间及其上的复合算子,给出了多重调和函数空间的对偶空间,刻画了该类空间上复合算子的有界性,紧性和Fredholm性.     

关于Banach空间中度量广义逆扰动定理的注记

Banach空间中线性算子的度量广义逆扰动定理具有重要应用,引入关注.在Acta Math Sinica English Series,2014(7)中对于从Banach空间X到Banach空间Y的有界线性算子T,在T的值域R(T)为切比雪夫子空间,T的零空间N(T)为切比雪夫子空间,且度量投影π_(N(T))为线性的条件下,得到二个有关非线性的广义逆扰动定理.本文证得:上述扰动定理结论的条件无需假定π_(N(T))的线性,只需假定N(T),R(T)分别为X,Y中的切比雪夫子空间即可.     

关于Lipschitz映射空间的可余子空间

该文研究Lipschitz映射空间作为一个Banach空间的结构性质，主要研究了它的闭子空间有界线性算子空间（赋予算子范数）在其中的可余性．     

局部Z-空间和Z-连续空间

对于一般广义子集系统Z,引入了局部Z-空间和Z-连续空间的概念,讨论了局部Z-空间的基本性质;基于收敛网,给出了局部Z-空间的等价刻画,证明了X为Z-连续空间当且仅当X为局部Z-空间。     

关于序列次可分解算子的不变子空间

得到了关于序列次可分解算子的一个不变子空间定理，推广了H.Mohebi和M.Rajiabalipour在1994年得到的一个不变子空间定理，并且举例说明存在l2上的有界线性算子T。它有无穷多个变子空间，但是它的不变子空间格Lat(T)不丰富。     

不变子空间问题的一个等价条件

本文得到了自反Banach空间X上有界线性算子全体所成的Banach代数的子代数的不变子空间问题的一个新的等价条件。     

Beurling定理的逆定理

设Ｈ为Ｈｉｌｂｅｒｔ空间．Ｔ为Ｈ上有界线性算子，对任何Ｔ的不变子空间Ｍ，称Ｔ具有Ｂｅｕｒｌｉｎｇ－性质．本文给出了次正常算子具有Ｂｅｕｒｌｉｎｇ－性质的充要条件．     

关于Nordgren的一个问题

本文证明了存在有界线性算子T使得T的弱预解集(WR(T)不是线性的,这回答了[1]中Nordgren等提出的一个未解决的问题。同时我们还讨论了有关WR(T)的若干基本性质。     

算子多项式的若干性质

本文讨论了多元算子多项式的几种保正号的性质，并由此得出关于正规算子不等式的转化定理。     

Z-代数格和Z-代数交结构

讨论Z-代数格,Z-代数交结构以及Z-代数闭包算子之间的关系,得到了格L上的Z-代数闭包算子与带顶元的Z-代数交结构之间存在一一对应关系,并且每一个Z-代数格都与带顶元的Z-代数交结构同构.     

Linear operators in finite dimensional probabilistic normed spaces

In this paper, we consider strongly bounded linear operators on a finite dimensional probabilistic normed space and define the topological isomorphism between probabilistic normed spaces. Then we prove that every finite dimensional probabilistic normed space which is a topological vector space is complete.     

Local dual spaces of Banach spaces of vector-valued functions

We show that is a local dual of , and is a local dual of , where is a Banach space. A local dual space of a Banach space is a subspace of so that we have a local representation of in satisfying the properties of the representation of in provided by the principle of local reflexivity.

     

On approximation of dual spaces and dual operators

We study the connection between equations which approximate an initial abstract linear equation and the adjoint one. We prove that the operator which is adjoint to the approximating one approximates the adjoint operator. As examples we consider adjoint linear integral equations and mutually dual linear programming problems.     

A characterization of normed spaces

We prove that the metric characterization of real normed spaces obtained by T. Oikhberg and H. Rosenthal can be obtained without a continuity assumption provided that the space is at least two-dimensional. In order to get this improvement we first need to understand the exceptional one-dimensional case.     

Composition operators on Dirichlet spaces and Bloch space

In this paper we give a Carleson measure characterization for the compact composition operators between Dirichlet type spaces. We use this characterization to show that every compact composition operator on Dirichlet type spaces is compact on the Bloch space.     

The dual of noncommutative Lorentz spaces

We prove some noncommutative analogues of the classical results about dual spaces of the classical Lorentz spaces.     

On an equivalence of topological vector space valued cone metric spaces and metric spaces

Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. Recently this has been applied by Du (2010) [14] to investigate the equivalence of vectorial versions of fixed point theorems of contractive mappings in generalized cone metric spaces and scalar versions of fixed point theorems in general metric spaces in usual sense. In this paper, we find out that the topology induced by topological vector space valued cone metric coincides with the topology induced by the metric obtained via a nonlinear scalarization function, i.e any topological vector space valued cone metric space is metrizable, prove a completion theorem, and also obtain some more results in topological vector space valued cone normed spaces.     

The sets of monomorphisms and of almost open operators between locally convex spaces

If the set of monomorphisms between locally convex spaces is not empty, then it is an open subset of the space of all continuous and linear operators endowed with the topology of the uniform convergence on the bounded sets if and only if the domain space is normable. The corresponding characterization for the set of almost open operators is also obtained; it is related to the lifting of bounded sets and to the quasinormability of the domain space. Other properties and examples are analyzed.

     

Laurent series for inversion of linearly perturbed bounded linear operators on Banach space

In this paper we find necessary and sufficient conditions for the existence of a Laurent series expansion with a finite order pole at the origin for the inverse of a linearly perturbed bounded linear operator mapping one Banach space to another. In particular we show that the inversion defines linear projections that separate the Banach spaces into corresponding complementary subspaces. We present two pertinent applications.     

Disjointly strictly singular inclusions of symmetric spaces

In this paper, the disjoint strict singularity of inclusions of symmetric spaces of functions on an interval is considered. A condition for the presence of a “gap” between spaces sufficient for the inclusion of one of these spaces into the other to be disjointly strictly singular is found. The condition is stated in terms of fundamental functions of spaces and is exact in a certain sense. In parallel, necessary and sufficient conditions for an inclusion of Lorentz spaces to be disjointly strictly singular (and similar conditions for Marcinkiewicz spaces) are obtained and certain other assertions are proved. Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 3–14, January, 1999.