Geometric Properties Of Banach Spaces

1;0Among all infinite dimensional Banach spaces, Hilbertrnspaces have the nicest and simplest geometric properties.rnIn Hilbert spaces the following two identitiesrnfor all andrn2) for all rnplay a key role in managing certain problems posed inrnHilbert spaces. It is our aim in this project to presentrnan important topic within the area of geometric propertiesrnof Banach spaces. In the first part of the paper, we exposernthese geometric properties most of which are well known.rnConsequently, to extend some of the Hilbert spacerntechniques to more general Banach spaces, analogues of thernidentities (1) and (2) have to be developed. For thisrndevelopment, the duality map which has become a mostrnimportant tool in nonlinear functional analysis plays arncentral role. It is the purpose of this project to mainlyrndiscuss the basic well-known facts on geometric propertiesrnof Banach spaces such as uniform convexity and uniformrnsmoothness. Finally, we present the duality maps in somernconcrete Banach spaces

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