Isometries in Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two (Monographs and Surveys in Pure and Applied Math)

✍ Scribed by Richard J. Fleming, James E. Jamison

• Publisher: Chapman and Hall/CRC
• Year: 2007
• Tongue: English
• Leaves: 245
• Series: Monographs and Surveys in Pure and Applied Math
• Category: Library

✦ Synopsis

A continuation of the authors’ previous book, Isometries on Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces.

Picking up where the first volume left off, the book begins with a chapter on the Banach–Stone property. The authors consider the case where the isometry is from C ₀( Q , X ) to C ₀( K , Y ) so that the property involves pairs ( X , Y ) of spaces. The next chapter examines spaces X for which the isometries on L^P ( μ , X ) can be described as a generalization of the form given by Lamperti in the scalar case. The book then studies isometries on direct sums of Banach and Hilbert spaces, isometries on spaces of matrices with a variety of norms, and isometries on Schatten classes. It subsequently highlights spaces on which the group of isometries is maximal or minimal. The final chapter addresses more peripheral topics, such as adjoint abelian operators and spectral isometries.

Essentially self-contained, this reference explores a fundamental aspect of Banach space theory. Suitable for both experts and newcomers to the field, it offers many references to provide solid coverage of the literature on isometries.

✦ Table of Contents

Cover......Page 1
Title......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 8
CHAPTER 7: The Banach-Stone Property......Page 12
CHAPTER 8: The Banach-Stone Property for Bochner Spaces......Page 62
CHAPTER 9: Orthogonal Decompositions......Page 94
CHAPTER 10: Matrix Spaces......Page 148
CHAPTER 11: Isometries of Norm Ideals of Operators......Page 170
CHAPTER 12: Minimal and Maximal Norms......Page 194
CHAPTER 13: Epilogue......Page 212
Bibliography......Page 224
Index......Page 240