We show that the Hilbert space is coarsely embeddable into any lp for 1 ≤ p < ∞. In particular, this yields new characterizations of embeddability of separable metric spaces into the Hilbert space. Coarse embeddings were defined by M. Gromov [Gr] to express the idea of inclusion in the large scale geometry of groups. G. Yu showed later that the case when a finitely generated group with a word l...

This paper studies asset pricing in arbitrage-free financial markets in general state space (both for frictionless market and for market with transaction cost). The mathematical formulation is based on a locally convex topological space for weakly arbitrage-free securities’ structure and a separable Banach space for strictly arbitragefree securities’ structure. We establish, for these two types...

In this paper, we shall present strong laws of large numbers (SLLN’s) for independent (not necessary identically distributed) fuzzy set-valued random variables whose base space is a separable Banach space or an Euclidean space, in the sense of the extended Hausdorff metric d∞ H .We apply the method to the sequence of independent identically distributed fuzzy set-valued random variables to give ...

We prove that a Lipschitz (or uniformly continuous) mapping f : X → Y can be approximated by smooth Lipschitz (resp. uniformly continuous) mapping, if X is a separable Banach space admitting a smooth Lipschitz bump and either X or Y is a C(K) space (resp. super-reflexive space). As a corollary we obtain also smooth approximation of C1-smooth mappings together with their first derivatives.

We extend the well-known characterizations of convergence in spaces $l_p$ ($1\le p<\infty$) $p$-summable sequence and $c_0$ vanishing sequences to a general characterization Banach space with Schauder basis obtain as instant corollaries an infinite-dimensional separable Hilbert $c$ convergent sequences.

Let Z be a fixed separable operator space, X ⊂ Y general separable operator spaces, and T : X → Z a completely bounded map. Z is said to have the Complete Separable Extension Property (CSEP) if every such map admits a completely bounded extension to Y ; the Mixed Separable Extension Property (MSEP) if every such T admits a bounded extension to Y . Finally, Z is said to have the Complete Separab...

We show that if Y is a separable subspace of a Banach space X such that both X and the quotient X/Y have Cp-smooth Lipschitz bump functions, and U is a bounded open subset of X, then, for every uniformly continuous function f : Y ∩U → R and every ε > 0, there exists a Cp-smooth Lipschitz function F : X → R such that |F (y)− f(y)| ≤ ε for every y ∈ Y ∩U . If we are given a separable subspace Y o...

1991 Abstract. A topological space X is called A-real compact, if every algebra homomorphism from A to the reals is an evaluation at some point of X, where A is an algebra of continuous functions. Our main interest lies on algebras of smooth functions. In AdR] it was shown that any separable Banach space is smoothly real compact. Here we generalize this result to a huge class of locally convex ...