Countable Direct Sums of Banach Spaces

Let (X_n) be a sequence of infinite-dimensional BANACH spaces. We prove that has a non-locally complete quotient if X₁ is not quasi-reflexive.     

套代数的直和算子集及可逆算子

本文研究了套代数的一个直和算子集X_N^φ,得到套代数的直和分解:τ(N)=D_N⊕X_N^φ,同时讨论了套代数中可逆算子的分布,得出套代数的对角D_N关于可逆算子是封闭的。特别地,当套为可数套时,套代数关于可逆性算子封闭的充要条件为φ(T)可逆。     

Integrability Properties of the Maximal Operator on Partial Sums of Fourier Series in Orlicz Spaces

Let S* (f be the majorant function of the partial sums of the trigonometric Fourier series of f. In this paper we consider the Orlicz space Lπ and give a generalization of Soria's result [S1]. Let π (t) be a concave function with some nice properties and . If there exists a positive constant a₀ < 1 such that then we have .     

算子空间的原子性

研究了算子空间的原子性.证明了算子空间V是原子当且仅当V是正合且有限内射; V内的任意一个有限维算子子空间是原子当且仅当V是原子且V内任意有限维算子子空间足V的完全补.因此作为推论,得到了无限维箅子空间V的任意有限维子空间是原子,则V是1-Hilbertian和1-齐次.     

算子空间的原子性

研究了算子空间的原子性.证明了算子空间V是原子当且仅当V是正合且有限内射; V内的任意一个有限维算子子空间是原子当且仅当V是原子且V内任意有限维算子子空间足V的完全补.因此作为推论,得到了无限维箅子空间V的任意有限维子空间是原子,则V是1-Hilbertian和1-齐次.     

Injectivity of Direct Sums

It is a well-known result that the direct sum of any family of injective modules over a Noetherian ring is injective. Conversely, if A is a ring with the property that the direct sum of any family of injective modules is injective H. Bass [1] has shown that A is Noetherian. The object of the present paper is to give necessary and sufficient conditions for the direct sum of a given family of modules over an arbitrary ring to be injective.     

Ordered Involutive Operator Spaces

This is a companion to recent papers of the authors; here we construct the ‘noncommutative Shilov boundary’ of a (possibly nonunital) selfadjoint ordered space of Hilbert space operators. The morphisms in the universal property of the boundary preserve order. As an application, we consider ‘maximal’ and ‘minimal’ unitizations of such ordered operator spaces.     

关于L-保序算子空间

借助ω-连通集,在L-保序算子空间中引入s-(ω1,ω2)-连续序同态和(ω1,ω2)-半连通序同态以及ω-半局部连通空间的概念,讨论了这两种序同态与(ω1,ω2)-连续序同态之间的关系;并关于s-(ω1,ω2)-连续序同态给出了ω-半局部连通空间的特征刻画。     

On Real Operator Spaces

During the last ten to fifteen years , a lot of progress has been achieved in the study of complex operator spaces. In this paper, we show that a corresponding theory can be developed for real operator spaces. With some appropriate modifications, many complex results still hold for real operator spaces.     

Barrelledness of Generalized Sums of Normed Spaces

Let (E _i ) _iI be a family of normed spaces and a space of scalar generalized sequences. The -sum of the family (E _i ) _iI of spaces is

On the Spectral Analysis of Direct Sums of Riemann-Liouville Operators in Sobolev Spaces of Vector Functions

Let J ^α _k be a real power of the integration operator J _k defined on the Sobolev space W ^k _p [0, 1]. We investigate the spectral properties of the operator defined on . Namely, we describe the commutant {A _k }′, the double commutant and the algebra Alg A _k . Moreover, we describe the lattices Lat A _k and HypLat A _k of invariant and hyperinvariant subspaces of A _k , respectively. We also calculate the spectral multiplicity  of A _k and describe the set Cyc A _k of its cyclic subspaces. In passing, we present a simple counterexample for the implication

Subspaces of Maximal Operator Spaces

We explore subspaces of maximal operator spaces ( submaximal spaces) and give a new characterization of such spaces. We show that the set of n-dimensional submaximal spaces is closed in the topology of c.b. distance, but not compact. We also investigate subspaces of MAX(L ) and prove that any homogeneous Hilbertian subspace of MAX(L ₁) is completely isomorphic to R + C.     

Bounded Reflexivity of Operator Spaces

We introduce a concept bounded reflexivity for a subspace of operators on a normed space. We explore the properties of bounded reflexivity, study the similarities and differences between bounded reflexivity and the usual reflexivity for a subspace of operators. As applications of bounded reflexivity, we give alternative proofs of some well known results about positivity and complete positivity of elementary operators.     

Zygmund 空间到 Bloch 空间上径向导数算子与积分型算子的乘积

设$H(\mathbb{B})$为单位球上全纯函数类,研究了单位球上 Zygmund 空间到 Bloch 空间上径向导数算子$\Re$与积分型算子$I_\varphi^g$乘积的有界性和紧性, 这里 $$ I_\varphi^g f(z)=\int_0^1 \Re f(\varphi(tz))g(tz)\frac{{\rm d}t}{t},\quad z\in\mathbb{B}, $$ 其中$g\in H(\mathbb{B}),\ g(0)=0$, $\varphi$ 是$\mathbb{B}$上全纯自映射.     

线性子空间的直和与直积

线性(子)空间的直和是线性代数中的重要概念,本文从泛映射性质的角度刻划线性(子)空间的直和与直积,证明有限个线性(子)空间的直和与直积同构,并将相关结论推广到无穷多个线性(子)空间的直和与直积.     

Operator Frames for Banach Spaces

In this paper, operator Bessel sequences, operator frames, Banach operator frames, Operator Riesz bases for Banach spaces and dual frames of an operator frame are introduced and discussed. The necessary and sufficient condition for a Banach space to have an operator frame, a Banach operator frame or an operator Riesz basis are given. In addition, operator frames and operator Riesz bases are characterized by the analysis operator of operator Bessel sequences.     

Bergman型空间到Bers型空间之加权复合算子

讨论了Bergman型空间H(p,μ)到Bers型空间H_β~∞、小Bers型空间H_(β,0)~∞上的加权复合算子,给出了加权复合算子有界性、紧性、弱紧性的充要条件,以及紧复合算子的角导数准则.本文还讨论了具有闭值域的加权复合算子,得到了一个充分条件.