Almost Surjective Epsilon-Isometry in The Reflexive Banach Spaces

Abstract

In this paper, we will discuss some applications of almost surjective epsilon-isometry mapping, one of them is in Lorentz space ( L_(p,q)-space). Furthermore, using some classical theorems of w star-topology and concept of closed subspace -complemented, for every almost surjective epsilon-isometry mapping  f : X to Y, where Y is a reflexive Banach space, then there exists a bounded linear operator   T : Y to X  with  such that

for every x in X.