uniformly in x as h—»0, we shall say briefly that/ belongs to Lip a. Following 4](1)) we shall say that/ belongs to a) uniformly as *—>0. a notation already used (see Zygmund lipa, 0<a<l, if \f(x+h)-f(x)\=o(\h It is a classical result of Lebesgue (see Zygmund [5, p. 61 ] ; hereafter this book will be denoted by T.S.) that if / belongs to Lip a and if sn denotes the nth partial sum of the Fourie...

We consider the general question of estimating decay of correlations for non-uniformly expanding maps, for classes of observables which are much larger than the usual class of Hölder continuous functions. Our results give new estimates for many non-uniformly expanding systems, including Manneville-Pomeau maps, many one-dimensional systems with critical points, and Viana maps. In many situations...

The purpose of this note is to present two elementary, but useful, facts concerning actions on uniformly convex spaces. We demonstrate how each of them can be used in an alternative proof of the triviality of the first Lp-cohomology of higher rank simple Lie groups, proved in [1]. Let G be a locally compact group with a compact generating set K ∋ 1, and let X be a complete Busemann non-positive...

Constructive properties of uniform convexity, strict convexity, near convexity, and metric convexity in real normed linear spaces are considered. Examples show that certain classical theorems, such as the existence of points of osculation, are constructively invalid. The methods used are in accord with principles introduced by Errett Bishop.

Weak and strong convergence theorems of three-step iterations are established for nonself asymptotically nonexpansive mappings in uniformly convex Banach space. The results obtained in this paper extend and improve the recent ones announced by Suantai 2005, Khan and Hussain 2008, Nilsrakoo and Saejung 2006, and many others.

For an operator bimodule X over von Neumann algebras A ⊆ B(H) and B ⊆ B(K), the space of all completely bounded A, B-bimodule maps from X into B(K,H), is the bimodule dual of X. Basic duality theory is developed with a particular attention to the Haagerup tensor product over von Neumann algebras. To X a normal operator bimodule Xn is associated so that completely bounded A, B-bimodule maps from...