We prove the following theorems: (1) Suppose that f : 2ω → 2ω is a continuous function and X is a Sierpiński set. Then (A) for any strongly measure zero set Y , the image f [X + Y ] is an s0-set, (B) f [X] is a perfectly meager set in the transitive sense. (2) Every strongly meager set is completely Ramsey null. This paper is a continuation of earlier works by the authors and by M. Scheepers (s...

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.

Let X and Y be Banach spaces. A set ᏹ of 1-summing operators from X into Y is said to be uniformly summing if the following holds: given a weakly 1-summing sequence (x n) in X, the series n T x n is uniformly convergent in T ∈ ᏹ. We study some general properties and obtain a characterization of these sets when ᏹ is a set of operators defined on spaces of continuous functions.

In general, the Gelfand widths cn(T ) of a map T between Banach spaces X and Y are not equivalent to the Gelfand numbers cn(T ) of T . We show that cn(T ) = cn(T ) (n ∈ N) provided that X and Y are uniformly convex and uniformly smooth, and T has trivial kernel and dense range. c ⃝ 2012 Elsevier Inc. All rights reserved.

Let A be a C*-algebra. Let z be the maximal atomic projection in A∗∗. By a theorem of Brown, x in A∗∗ has a continuous atomic part, i.e. zx = za for some a in A, whenever x is uniformly continuous on the set of pure states of A. Let L be a closed left ideal of A. Under some additional conditions, we shall show that for any x in A∗∗, x has a continuous atomic part modulo L∗∗, i.e. zx + L∗∗ = za ...

Let A be a C*-algebra. Let z be the maximal atomic projection and p a closed projection in A∗∗. It is known that x in A∗∗ has a continuous atomic part, i.e. zx = za for some a in A, whenever x is uniformly continuous on the set of pure states of A. Under some additional conditions, we shall show that if x is uniformly continuous on the set of pure states of A supported by p, or its weak* closur...

A fading-memory system is a system that tends to forget its input asymptotically over time. It has been shown that discrete-time fading-memory systems can be uniformly approximated arbitrarily closely over a set of bounded input sequences simply by uniformly approximating sufficiently closely either the external or internal representation of the system. In other words, the problem of uniformly ...

We study the behavior of inexact products uniformly continuous self-mappings a complete metric space that is and bounded on sets. It shown previously established convergence theorems for non-expansive mappings continue to hold even under presence computational errors.