Geometric Properties of Banach Spaces

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Addis Ababa University


1;0Among all infinite dimensional Banach spaces, Hilbert spaces have the nicest and simplest geometric properties. In Hilbert spaces the following two identities for all and 2) for all play a key role in managing certain problems posed in Hilbert spaces. It is our aim in this project to present an important topic within the area of geometric properties of Banach spaces. In the first part of the paper, we expose these geometric properties most of which are well known. Consequently, to extend some of the Hilbert space techniques to more general Banach spaces, analogues of the identities (1) and (2) have to be developed. For this development, the duality map which has become a most important tool in nonlinear functional analysis plays a central role. It is the purpose of this project to mainly discuss the basic well-known facts on geometric properties of Banach spaces such as uniform convexity and uniform smoothness. Finally, we present the duality maps in some concrete Banach spaces



Geometric Properties