Property A and the operator norm localization property for discrete metric spaces

The Amalgamation Property for G-metric Spaces

Let G be a (totally) ordered (abelian) group. A Gmetric space (X, p) consists of a nonempty set A"and a G-metric />: XxX->-G (satisfying the usual axioms of a metric, with G replacing the ordered group of real numbers). That the amalgamation property holds for the class of all metric spaces is attributed, by Morley and Vaught, to Sierpiñski. The following theorem is proved. Theorem. The class o...

Metric sparsification and operator norm localization

We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. A metric space X is said to have operator norm localization property if there exists 0 < c ≤ 1 such that for every r > 0, there is R > 0 for which, if ν is a positive locally finite Borel measure on X, H is a separable infinite dimensional Hilbert space and T is a bounded ...

Orlicz property of operator spaces and eigenvalue estimates

As is well known absolute convergence and unconditional convergence for series are equivalent only in finite dimensional Banach spaces. Replacing the classical notion of absolutely summing operators by the notion of 1 summing operators

The ¿-norm Extension Property for Banach Spaces1

On the shadowing property of nonautonomous discrete systems

In this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e. nonautonomous discrete dynamical systems. We investigate the relation of  weak contractions with shadowing and h-shadowing property.