Central Subspaces of Banach Spaces

In this paper we study Banach spaces that admit weighted Chebyshev centres for finite sets. Such spaces have been extensively studied recently by Veselý using the approach of finitely intersecting balls. Following his approach we exhibit large classes of Banach spaces that have this property. Certain stability results for spaces of vector valued continuous and Bochner integrable functions are also obtained.     

Orthogonally Complemented Subspaces in Banach Spaces

In this paper, we extend the Moreau (Riesz) decomposition theorem from Hilbert spaces to Banach spaces. Criteria for a closed subspace to be (strongly) orthogonally complemented in a Banach space are given. We prove that every closed subspace of a Banach space X with dim X ≥ 3 (dim X ≤ 2) is strongly orthognally complemented if and only if the Banach space X is isometric to a Hilbert space (resp. strictly convex), which is complementary to the well-known result saying that every closed subspace of a Banach space X is topologically complemented if and only if the Banach space X is isomorphic to a Hilbert space.     

The Degree of Weakly Discretely Generated Spaces

A space X is discretely generated at a point \({x \in X}\) if for any \({A \subseteqq X}\) with \({x \in \textsf{cl}(A)}\) , there exists a discrete set \({D \subseteqq A}\) such that \({x \in \textsf{cl}(D)}\) . The space X is discretely generated if it is discretely generated at every point \({x \in X}\) . We say that X is weakly discretely generated if for any non-closed set \({A \subseteqq X}\) , there exists a discrete set \({D \subseteqq A}\) such that \({\textsf{cl}(D) \setminus A \neq \emptyset}\) . New results about these properties in the classes of pseudocompact and ?ech-complete spaces are obtained and a theorem of Ivanov and Osipov concerning the ordinal function idc is generalized to the class of ?ech-complete spaces.     

Operators on Subspaces of Hereditarily Indecomposable Banach Spaces

We show that if X is a complex hereditarily indecomposable space,then every operator from a subspace Y of X to X is of the formI + S, where I is the inclusion map and S is strictly singular.1991 Mathematics Subject Classification 46B20, 47B99.     

Weakly Sub-Gaussian Random Elements in Banach Spaces

We give a survey of properties of weakly sub-Gaussian random elements in infinite-dimensional spaces. Some new results and examples are also given. __________ Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 9, pp. 1187–1208, September, 2005.     

Invariant Subspaces of Positive Quasinilpotent Operators on Ordered Banach Spaces

In this paper we find invariant subspaces of certain positive quasinilpotent operators on Krein spaces and, more generally, on ordered Banach spaces with closed generating cones. In the later case, we use the method of minimal vectors. We present applications to Sobolev spaces, spaces of differentiable functions, and C*-algebras.      

Strongly Generated Banach Spaces and Measures of Noncompactness

To generalize the Hausdorff measure of noncompactness to other classes of bounded sets (like e. g. conditionally weakly compact or Asplund sets), we introduce Grothendieck classes. We deduce integral inequalities for quantities (called Grothendieck measures) related to these classes. As a by-product, we can answer a question concerning the measure of noncompactness for linear T : X → Y introduced in [14], and generalize a theorem about weak solutions of differential equations in Banach spaces.     

A Note on Compactly Generated Co-t-Structures

The idea of a co-t-structure is almost ‘dual’ to that of a t-structure, but with some important differences. This note establishes co-t-structure analogues of Beligiannis and Reiten's corresponding results on compactly generated t-structures.     

复平面上解析Banach空间的拟不变子空间

讨论复平面上解析Banach空间具有任意指标的拟不变子空间的存在性问题.首先给出一类复平面上解析Banach空间存在任意指标拟不变子空间的判定定理.作为应用,证明了Fock型空间F~p(C)={f∈Hol(C):1/π∫_C|f(z)|~pe~(-|z|~2)dA(z)+∞,1≤p+∞}与Hilbert空间H={f∈Hol(C):1/π∫_C|f(z)|~2e~(-|z|)dA(z)+∞}具有任意指标的拟不变子空间.     

The Structure of Finitely Generated Shift-Invariant Subspaces in Super Hilbert Spaces

We study the structure of finitely generated shift-invariant subspaces with generators from the super Hilbert space L ²(? ^d )^(N). We give a characterization for these subspaces. Moreover, we show that every finitely generated shift-invariant subspace possesses a tight frame. We also give a necessary and sufficient condition for such a space to be principal. Our results generalize similar ones for which generators are from L ²(? ^d ).     

Banach空间中的弱凸集和W-太阳集

本文在光滑Banach空间的框架下,引进弱凸集和W-太阳集的概念,研究它们性质,并给出了在逼近问题中的应用.     

Banach空间上套代数的弱闭Jordan模

设■为Banach空间X上的套,D为Alg■的弱闭Jordan模.若对任意N∈■,dim(N/■_)≠1与N拓扑可补至少有一个成立,则■必为Alg■的模.     

Closed Complemented Subspaces of Banach Spaces and Existence of Bounded Quasi-linear Generalized Inverses

In this article, an equivalent condition for the existence of a bounded quasi-linear (BQL) generalized inverse of a closed linear operator with respect to projector between two Banach spaces is given. Using the BQL generalized inverse, we give a necessary and su?cient condition for a closed linear subspace in a Banach space to be complemented. Finally, an application of the main results to the Saddle–Node bifurcation theorem from multiple eigenvalues in nonlinear analysis is given.     

Compactly Generated Relative Stable Categories

Let G be a finite group. The stable module category of G has been applied extensively in group representation theory. In particular, it has been used to great effect that it is a triangulated category which is compactly generated by the class of finitely generated modules. Let H be a subgroup of G. It is possible to define a stable module category of G relative to H. This is also a triangulated category, but no non-trivial examples have been known where it was compactly generated. While the finitely generated modules are compact objects, they do not necessarily generate the category. We show that the relative stable category is compactly generated if the group algebra of H has finite representation type. In characteristic p, this is equivalent to the Sylow p-subgroups of H being cyclic.     

On Subspaces and Quotients of Banach Spaces C(K, X)

 We study the relation of to the subspaces and quotients of Banach spaces of continuous vector-valued functions , where K is an arbitrary dispersed compact set. More precisely, we prove that every infinite dimensional closed subspace of totally incomparable to X contains a copy of complemented in . This is a natural continuation of results of Cembranos-Freniche and Lotz-Peck-Porta. We also improve our result when K is homeomorphic to an interval of ordinals. Next we show that complemented subspaces (resp., quotients) of which contain no copy of are isomorphic to complemented subspaces (resp., quotients) of some finite sum of X. As a consequence, we prove that every infinite dimensional quotient of which is quotient incomparable to X, contains a complemented copy of . Finally we present some more geometric properties of spaces. Received 8 November 2000; in revised form 7 December 2001     

Banach空间中弱收敛序列系数的估计

利用.Jordan—von Neumann型常数C_t~′(X),C_(-∞)(X)和弱正交系数μ(X)对Banach空间中的弱收敛序列系数WCS(X)进行了估计,从而得到空间具有正规结构的充分条件,这些结论推广了最近一些文献中的结果.同时,还计算了Bynum空间l_(2.∞)。中上述常数的取值,来说明我们给定的条件是一个严格的推广.