Geometric Properties of Banach Spaces
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Date
2012-01
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Addis Ababa University
Abstract
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
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Geometric Properties