Stability in interpolation of families of Banach spaces

Weak Interpolation in Banach Spaces

Stability of generalized QCA-functional equation in P-Banach spaces

In  this paper, we investigate the generalizedHyers-Ulam-Rassias stability for the quartic, cubic and additivefunctional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k in mathbb{Z}-{0,pm1}$) in $p-$Banach spaces.

Stability in Banach Spaces

Many questions in Banach space theory are of the type: Let X be an infinite dimensional Banach space. Let (P) be a property. Does X contain a closed infinite dimensional subspace Y with (P)? Sometimes the question takes the form: If X has a certain property (Q), does X contain Y having (P)? Of course the answers and solutions (if known) depend upon the particular properties involved. But there ...

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...

Embeddings of Levy Families into Banach Spaces

We prove that if a metric probability space with a usual concentration property embeds into a Banach space X, then X has a proportional Euclidean subspace. In particular, this yields a new characterization of weak cotype 2. We also find optimal lower estimates on embeddings spaces with concentration properties (i.e. uniformly convex spaces) into l ∞, thus providing an ”isomorphic” extension to ...