Norm Derivatives And Characterizations Of Inner Product Spaces
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A01=Claudi Alsina
A01=Justyna Sikorska
A01=M Santos Tomas
Author_Claudi Alsina
Author_Justyna Sikorska
Author_M Santos Tomas
Banach Spaces
Category=PBKF
Characterizations of Norms
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Functional Equations
Geometry in Normed Spaces
Hilbert Spaces
Inner Products
Norm Derivatives
Norms
Product details
- ISBN 9789814287265
- Publication Date: 02 Dec 2009
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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The book provides a comprehensive overview of the characterizations of real normed spaces as inner product spaces based on norm derivatives and generalizations of the most basic geometrical properties of triangles in normed spaces. Since the appearance of Jordan-von Neumann's classical theorem (The Parallelogram Law) in 1935, the field of characterizations of inner product spaces has received a significant amount of attention in various literature texts. Moreover, the techniques arising in the theory of functional equations have shown to be extremely useful in solving key problems in the characterizations of Banach spaces as Hilbert spaces.This book presents, in a clear and detailed style, state-of-the-art methods of characterizing inner product spaces by means of norm derivatives. It brings together results that have been scattered in various publications over the last two decades and includes more new material and techniques for solving functional equations in normed spaces. Thus the book can serve as an advanced undergraduate or graduate text as well as a resource book for researchers working in geometry of Banach (Hilbert) spaces or in the theory of functional equations (and their applications).
