Banach空间的p-弱近似性质

给出了Banach空间的p-弱近似性质和p-有界弱近似性质的定义,获得了这些性质的一些刻画.利用这些刻画证明了如果一个Banach空间X的对偶空间X~*有p-弱近似性质(或p-有界弱近似性质),则X有p-弱近似性质(或p-有界弱近似性质),在一般情况下反之不成立.     

BMO鞅空间上极大算子与均方算子的有界性

本文证明了,q 均方算子在 X 值 BMO 鞅空间上是有界的当且仅当 X 同构于 q凸 Banach 空间。此外给出了极大算子与 q 均方算子的 BMO 范数,讨论了鞅空间(?)_q 与BMO_q 的相互包含关系并以此刻划了 Banach 空间的几何性质。     

Lp-空间中的正多线性可和算子

本文证明,当1≤q≤2时L^q-空间上的正多线性2-可和算子都是正多线性1-可和的.若1 q-空间上的正多线性p-可和算子都是正多线性1-可和的;进一步地,若像空间有Radon-Nikodym性质,则L^q-空间上的多线性算子是正多线性p-可和的当且仅当其能表示为L^p-空间上的函数.     

关于有界闭凸集上的弱滴性质的注记

证明了“若K是Banach空间X中的有界闭凸集,0∈intK,则K有弱滴性质当且仅当K⁰有(WS)性质.”从而证明了文[1]中提出的一个问题.     

超Sober空间与k-有界Sober空间的性质

讨论了超Sober空间与k-有界Sober空间的一些性质,厘清相关拓扑之间的关系.特别地证明了一个空间是超Sober空间当且仅当其Smyth上幂空间为超Sober空间;任意一族k-有界Sober空间的积空间为k-有界Sober空间.     

超Sober空间与k-有界Sober空间的性质北大核心

讨论了超Sober空间与k-有界Sober空间的一些性质,厘清相关拓扑之间的关系.特别地证明了一个空间是超Sober空间当且仅当其Smyth上幂空间为超Sober空间;任意一族k-有界Sober空间的积空间为k-有界Sober空间.     

Banach空间上可约化算子的谱分解

本文从谱分解的角度讨论了Banach空间上可约化算子,谱算子和可分解算子间的关系,并证明了以下主要结果: 1.设T∈B(X)是完全谱可约化的可分解算子,则对每个F∈B,成立着 2.设T∈B(X),则T是谱算子当且仅当T是具有性质(B)的完全谱可约化的可分解算子。     

Banach空间的凸性、光滑性与逼近紧性再探究

本文首先定义了Banach空间中的一种新性质,Q性质.并且证明了Banach空间X中的每个闭凸集是逼近紧Chebyshev集当且仅当X满足Q性质;其次证明X是自反的中点局部一致凸空间当且仅当X具有Q性质,其证明运用到了Banach空间几何理论的一些巧妙方法.     

Ｐ型基和良性有界算子

在自反Ｂａｎａｃｈ空间上一个有界线性算子是（Ｂ）型良性有界的当且仅当它的共扼算子也是（Ｂ）型的。但在非自反Ｂａｎａｃｈ空间上这种性质不成立。本文证明在一大类非自反Ｂａｎａｃｈ空间上总存在一个（Ｂ）型良性有界线性算子，它的共扼算子不是（Ｂ）型的。同时也证明了在具有基的Ｂａｎａｃｈ空间上，任何Ｐ型基序列一定有一个子序弄能够扩张成该空间的一个基。     

Banach空间中的有界算子4子空间系统

本文研究Banach空间上有界算子4子空间系统S_T,说明S_T与S_T同构的充要条件是T与T相似,也说明S_T是不可分解的的充要条件是T是强不可约的,最后说明当Banach空间X的共轭空间X~*w~*可分时,X⊕X中存在不可数多个两两不同构的不可分解的有界算子4子空间系统.这些结果是Hilbert空间上相应结果到Banach空间上的推广与补充.     

The asymptotically commuting bounded approximation property of Banach spaces

We introduce and study the asymptotically commuting bounded approximation property of Banach spaces. This property is, e.g., enjoyed by any dual space with the bounded approximation property. The principal result is the following: if a Banach space X has the asymptotically λ-commuting bounded approximation property, then X is saturated with locally λ-complemented separable subspaces enjoying the λ-commuting bounded approximation property.     

The bounded approximation property for spaces of holomorphic mappings on infinite dimensional spaces

We study the bounded approximation property for spaces of holomorphic functions. We show that if U is a balanced open subset of a Fréchet–Schwartz space or (DFM )‐space E , then the space ??(U ) of holomorphic mappings on U , with the compact‐open topology, has the bounded approximation property if and only if E has the bounded approximation property. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-space problems for the bounded compact approximation property

In this paper, the notion of the bounded compact approximation property (BCAP) of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of L∞ with the BCAP, then L∞/X has the BCAP. We also show that X* has the λ-BCAP with conjugate operators if and only if the pair (X, Y) has the λ-BCAP for each finite codimensional subspace Y∈X. Let M be a closed subspace of X such that M⊥ is complemented in X*. If X has the (bounded) approximation property of order p, then M has the (bounded) approximation property of order p.     

Dual problems for weak and quasi approximation properties

It is shown that for the separable dual X^∗ of a Banach space X if X^∗ has the weak approximation property, then X has the metric quasi approximation property. Using this it is shown that for the separable dual X^∗ of a Banach space X the quasi approximation property and metric quasi approximation property are inherited from X^∗ to X and for a separable and reflexive Banach space X, X having the weak approximation property, bounded weak approximation property, quasi approximation property, metric weak approximation property, and metric quasi approximation property are equivalent. Also it is shown that the weak approximation property, bounded weak approximation property, and quasi approximation property are not inherited from a Banach space X to X^∗.     

Compact and Weakly Compact Homomorphisms on Fréchet Algebras of Holomorphic Functions

We study homomorphisms between Fréchet algebras of holomorphic functions of bounded type. In this setting we prove that any pointwise bounded homomorphism into the space of entire functions of bounded type is rank one. We characterize up to the approximation property of the underlying Banach space, the weakly compact composition operators on H_b(V), V absolutely convex open set.     

The metric approximation property,norm-one projections and intersection properties of balls

We show that ifE is a Banach space with the Radon-Nikodym property thenE has the metric approximation property if and only if the space of finite rank operators is locally complemented in the space of bounded operators.     

Distortion and stability of the fixed point property for non-expansive mappings

Let X be a Banach space. We say that X satisfies the fixed point property (weak fixed point property) if every non-expansive mapping defined from a convex closed bounded (convex weakly compact) subset of X into itself has a fixed point. We say that X satisfies the stable fixed point property (stable weak fixed point property) if the same is true for every equivalent norm which is close enough to the original one. Denote by P(X) the set formed by all equivalent norms with the topology of the uniform convergence on the unit ball of X. We prove that the subset of P(X) formed by the norms failing the fixed point property is dense in P(X) when X is a non-distortable space which fails the fixed point property. In particular, no renorming of ?₁ can satisfy the stable fixed point property. Furthermore, we show some examples of distortable spaces failing the weak fixed point property, which can be renormed to satisfy the stable weak fixed point property. As a consequence we prove that every separable Banach space can be renormed to satisfy the stable weak fixed point property.     

ON THE SETS OF GATEAUX NON-DIFFERENTIABILITY OF LIPSCHITZ ISOMORPHISM BETWEEN BANACH SPACES＊t

We prove that for every Lipschitz isomorphism f from a separable Hilbert space H to a Banach space Y with Radon-Nikodym property, there is a bounded surjective ...     

Compact adjoint operators and approximation properties

This paper is concerned with the space of all compact adjoint operators from dual spaces of Banach spaces into dual spaces of Banach spaces and approximation properties. For some topology on the space of all bounded linear operators from separable dual spaces of Banach spaces into dual spaces of Banach spaces, it is shown that if a bounded linear operator is approximated by a net of compact adjoint operators, then the operator can be approximated by a sequence of compact adjoint operators whose operator norms are less than or equal to the operator norm of the operator. Also we obtain applications of the theory and, in particular, apply the theory to approximation properties.