Random products of contractions in metric and Banach Spaces

Suppose (X, d) is a metric space and {T₀,…, T_N} is a family of quasinonexpansive self-mappings on X. We give conditions sufficient to guarantee that every possible iteration of mappings drawn from {T₀,…, T_N} converges. As a consequence, if C₀,…, C_N are closed convex subsets of a Hilbert space with nonempty intersection, one of which is compact, and the proximity mappings are iterated in any order (provided only that each is used infinitely often), then the resulting sequence converges strongly to a point of the common intersection.     

Banach空间上的Banach框架及原子分解的稳定性

讨论了Banach空间上的Banach框架及原子分解的稳定性,得到了一些新的结果,并给出一些已知结果的推论.     

The Monge Problem in Banach Spaces

In this paper, we generalize the Kantorovich functional to K?the-spaces for a cost or a profit function. We examine the convergence of probabilities with respect to this functional for some K?the-spaces. We study the Monge problem: Let be a K?the-space, P and Q two Borel probabilities defined on a Polish space M and a cost function . A K?the functional is defined by (P, Q) = inf where is the law of X. If c is a profit function, we note . (P, Q) = sup Under some conditions, we show the existence of a Monge function, φ, such that , or .      

The Steiner Subratio in Banach Spaces

Mathematical Notes - For every n = 2, 3,…, the minimum of the Steiner subratio is found for n-point sets in Banach spaces, and an example of a Banach space is constructed for which this...     

Banach Spaces with the PC Property

A Banach space X possesses the PC (point of continuity) property if for any w-closed bounded subset A ? X the identity map (A,w)→(A, ∥ ? ∥) has a point of continuity (w is the weak topology in X). We deduce some criteria for Banach spaces to have the PC property and describe (for dual Banach spaces) relationships between spaces possessing the PC property and spaces possessing the RN or the WRN property.

     

Banach algebras with unique uniform norm

Commutative semisimple Banach algebras that admit exactly one uniform norm (not necessarily complete) are investigated. This unique uniform norm property is completely characterized in terms of each of spectral radius, Silov boundary, set of uniqueness, semisimple norms; and its connection with recently investigated concepts like spectral extension property, multiplicative Hahn Banach extension property and permanent radius are revealed. Several classes of Banach algebras having this property as well as those not having this property are discussed.

     

Banach Spaces which are Radon Spaces with the Weak Topology

In this paper, Schachermayer's Theorem [6] is improved by showingthat a WCG Banach space whose density is of measure zero isa Radon space with the weak topology (weak-Radon). We also considerother conditions under which a Banach space is a weak-Radonspace.     

Spaces with a uniformly continuous metric projection

This paper contains a characterization of spaces in which the metric projection is uniformly continuous on the class of convex existence sets.     

非自反Banach空间中的度量投影

该文给出非自反Banach空间中一类超平面上度量投影的表达式．在近严格凸Banach空间中,研究了它们的连续性．对于对偶Banach空间X*,给出弱*闭子集上度量投影的一些连续性结果．     

The Geometry of Convex Transitive Banach Spaces

Throughout this paper, X will denote a Banach space, S=S(X)and B=B(X) will be the unit sphere and the closed unit ballof X, respectively, and G=G(X) will stand for the group of allsurjective linear isometries on X. Unless explicitly statedotherwise, all Banach spaces will be assumed to be real. Nevertheless,by passing to real structures, the results remain true for complexspaces. 1991 Mathematics Subject Classification 46B04, 46B10,46B22.     

Banach空间中推广的Roper-Suffridge算子(英文)

In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spaces.     

Banach空间的保持端点

在本文中，我们定义了（Ｒ１），（Ｒ２），（Ｒ３）和ｗＭＬＵＲ，它们是一些与严格凸较接近且所有端点都是保持端点的凸性。我们还讨论了它们的性质以及它们之间的相互关系。     

Totally Incomparable Banach Spaces and Three-Space Banach Space Ideals

In this paper we present four methods to generate three-space BANACH space ideals. They are based on the concept of total incomparability of H. P. ROSENTHAL and on a dual concept, total coincomparability, which is here introduced. We use the assertion that the sum of two totally incomparable closed subspaces of a BANACH space is norm-closed, which is shown by means of an easier and more natural proof than that of ROSENTHAL [10], and an analogous property about the total coincomparability. Several well-known ideals are obtained with the above methods, and so they are three-space ideals.     

Wavelets in Banach Spaces

We describe a construction of wavelets (coherent states) in Banach spaces generated by admissible group representations. Our main targets are applications in pure mathematics while connections with quantum mechanics are mentioned. As an example, we consider operator-valued Segal–Bargmann-type spaces and the Weyl functional calculus.     

Real Banach Spaces with Numerical Index 1

We show that an infinite-dimensional real Banach space withnumerical index 1 satisfying the Radon–Nikodym propertycontains l₁. It follows that a reflexive or quasi-reflexivereal Banach space cannot be re-normed to have numerical index1, unless it is finite-dimensional. 1991 Mathematics SubjectClassification 46B20.     

Very Convex Banach Spaces

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K—very Smooth Banach Spaces

We introduce the notion of K-very smoothness which is a generalization of very smoothness in Banach spaces. A necessary and sufficient condition for a Banach space to be K-very smooth is obtained. We also consider some relations between K-very smoothness and other geometrical notions.