FULLY CONVEX NORMED LINEAR SPACES

Porosity of Convex Nowhere Dense Subsets of Normed Linear Spaces

and Applied Analysis 3 Definition 2.4. M is called c-porous if for any x ∈ X and every r > 0, there are y ∈ B x, r and φ ∈ X∗ \ {0} such that { z ∈ X : φ z > φy ∩M ∅. 2.2 C-porosity turns out to be the suitable notion to describe the smallness of convex nowhere dense sets see Proposition 2.5 and is a stronger form of 0-angle porosity x ∈ X instead x ∈ M . Indeed, consider the unit sphere S of a...

Refinements of s-Orlicz Convex Functions in Normed Linear Spaces

On asphericity of convex bodies in linear normed spaces

In 1960, Dvoretzky proved that in any infinite dimensional Banach space X and for any [Formula: see text] there exists a subspace L of X of arbitrary large dimension ϵ-iometric to Euclidean space. A main tool in proving this deep result was some results concerning asphericity of convex bodies. In this work, we introduce a simple technique and rigorous formulas to facilitate calculating the asph...

Positively Convex Modules and Ordered Normed Linear Spaces

A positively convex module is a non-empty set closed under positively convex combinations but not necessarily a subset of a linear space. Positively convex modules are a natural generalization of positively convex subsets of linear spaces. Any positively convex module has a canonical semimetric and there is a universal positively affine mapping into a regularly ordered normed linear space and a...

Embedding normed linear spaces into $C(X)$

‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...