Sharp Corner Points and α - large Families with a Countable Infinite Number on Banach Spaces

Abstract

We begin using some geometric methods to study The isometric problem in general real Banach spaces. Moreover we study the “sharp corner points” in many classical Banach spaces and solve isometric extension problem . We show the existence of such families on the cardinal number and study their properties. We show that the Banach spaces are large subspaces of the essential Hilbert spaces. The Banach space with a countable infinite number of complex structures was considered.