Isometries on Banach spaces : vector-valued function spaces : volume 2 / Richard J. Fleming, James E. Jamison.

Format:

Book

Author/Creator:

Fleming, Richard J.

Contributor:

Jamison, James E.

Louis A. Duhring Fund.

Series:

Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; 138.

Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; 138

Language:

English

Subjects (All):

Banach spaces.

Function spaces.

Operator spaces.

Isometrics (Mathematics).

Physical Description:

ix, 234 pages ; 25 cm.

Place of Publication:

Boca Raton, FL : CRC Press, [2008]

Summary:

A continuation of the authors' previous book, Isometries on Banach Spaces: Vector-valued Function 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[subscript 0](Q, X) to C[subscript 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[superscript p]([mu], 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.

Contents:

Chapter 7 The Banach-Stone Property 1

7.2 Strictly Convex Spaces and Jerison's Theorem 3

7.3 M Summands and Cambern's Theorem 10

7.4 Centralizers, Function Modules, and Behrends' Theorem 18

7.5 The Nonsurjective Vector-Valued Case 28

7.6 The Nonsurjective Case for Nice Operators 36

Chapter 8 The Banach-Stone Property for Bochner Spaces 51

8.2 L[superscript p] Functions with Values in Hilbert Space 53

8.3 L[superscript p] Functions with Values in Banach Space 63

8.4 L[superscript 2] Functions with Values in a Banach Space 72

Chapter 9 Orthogonal Decompositions 83

9.2 Sequence Space Decompositions 84

9.3 Hermitian Elements and Orthonormal Systems 97

9.4 The Case for Real Scalars: Functional Hilbertian Sums 105

9.5 Decompositions with Banach Space Factors 115

Chapter 10 Matrix Spaces 137

10.2 Morita's Proof of Schur's Theorem 138

10.3 Isometries for (p, k) Norms on Square Matrix Spaces 140

10.4 Isometries for (p, k) Norms on Rectangular Matrix Spaces 147

Chapter 11 Isometries of Norm Ideals of Operators 159

11.2 Isometries of C[subscript p] 160

11.3 Isometries of Symmetric Norm Ideals: Sourour's Theorem 166

11.4 Noncommutative L[superscript p] Spaces 172

Chapter 12 Minimal and Maximal Norms 183

12.2 An Infinite-Dimensional Space with Trivial Isometries 184

12.3 Minimal Norms 186

12.4 Maximal Norms and Forms of Transitivity 190

13.1 Reflexivity of the Isometry Group 201

13.2 Adjoint Abelian Operators 204

13.3 Almost Isometries 207

13.4 Distance One Preserving Maps 210

13.5 Spectral Isometries 210

13.6 Isometric Equivalence 211

13.7 Potpourri 212.

Notes:

A continuation the authors' previous book: Isometries on Banach spaces : function spaces. Boca Raton : Chapman & Hall/CRC, c2003.

Includes bibliographical references (pages 213-227) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Louis A. Duhring Fund.

ISBN:

9781584883869

1584883863

OCLC:

173502826