C 11 Contractions are reflexive. II

A non-reflexive Banach space with all contractions mean ergodic

We construct on any quasi-reflexive of order 1 separable real Banach space an equivalent norm, such that all contractions on the space and all contractions on its dual are mean ergodic, thus answering negatively a question of Louis Sucheston.

Uniformly convex Banach spaces are reflexive - constructively

We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the MilmanPettis theorem that uniformly convex Banach spaces are reflexive. Our aim in this note is to present a fully constructive analysis of the Milman-Pettis theorem [11, 12, 9, 13]: a uniformly convex Banach space is reflexive. First, t...

Piecewise Contractions Are Asymptotically Periodic

We show that, given a finite partition of the plane C such that the map G acts as a linear contraction on each part, for almost every choice of parameters every orbit of G is (asymptotically) periodic.

Best Proximity Points of Cyclic φ-Contractions on Reflexive Banach Spaces

On the Spectra of C„ Contractions

We give a complete characterization of the closed subsets of the complex plane that can serve as spectra of completely nonunitary contractions of class Cu. Let Jfbe a complex Hilbert space, and denote by £^(Jff) the algebra of all (continuous, linear) operators acting onJf. An operator T g Sí'(Jíf) is a contraction if \\T\\ < 1. A contraction T g J¡f( Jf ) is said to be a C,,-contraction if lim...