Dvoretzky's theorem for quasi-normed spaces

A Bernstein-Markov Theorem for Normed Spaces

Let X and Y be real normed linear spaces and let φ : X → R be a non-negative function satisfying φ(x+ y) ≤ φ(x) + ‖y‖ for all x, y ∈ X. We show that there exist optimal constants cm,k such that if P : X → Y is any polynomial satisfying ‖P (x)‖ ≤ φ(x)m for all x ∈ X, then ‖D̂kP (x)‖ ≤ cm,kφ(x) whenever x ∈ X and 0 ≤ k ≤ m. We obtain estimates for these constants and present applications to polyno...

Quotients of Finite-dimensional Quasi-normed Spaces

We study the existence of cubic quotients of finite-dimensional quasi-normed spaces, that is, quotients well isomorphic to `∞ for some k. We give two results of this nature. The first guarantees a proportional dimensional cubic quotient when the envelope is cubic; the second gives an estimate for the size of a cubic quotient in terms of a measure of nonconvexity of the quasi-norm.

The Extension of the Finite-Dimensional Version of Krivine’s Theorem to Quasi-Normed Spaces

In 1980 D. Amir and V. D. Milman gave a quantitative finitedimensional version of Krivine’s theorem. We extend their version of the Krivine’s theorem to the quasi-convex setting and provide a quantitative version for p-convex norms. Recently, a number of results of the Local Theory have been extended to the quasi-normed spaces. There are several works [Kal1, Kal2, D, GL, KT, GK, BBP1, BBP2, M2]...

Bishop-Phelps type Theorem for Normed Cones

In this paper the notion of  support points of convex sets  in  normed cones is introduced and it is shown that in a  continuous normed cone, under the appropriate conditions, the set of support points of a  bounded Scott-closed convex set is nonempty. We also present a Bishop-Phelps type Theorem for normed cones.

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition