Isometries in Banach Spaces: Volume 2

Isometries in Banach Spaces: Volume 2 : Vector-Valued Function Spaces and Operator Spaces

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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 C0(Q, X) to C0(K, Y) so that the property involves pairs (X, Y) of spaces. The next chapter examines spaces X for which the isometries on LP(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 more

Product details

  • Hardback | 248 pages
  • 170 x 234 x 24mm | 539.77g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 1584883863
  • 9781584883869
  • 2,497,258

Review quote

About volume one," Isometries on Banach Spaces: Function Spaces: " "This is a very well written book. The authors have done a remarkable job in collecting this material and in exposing it in a very clear style. It will be an important reference tool for analysts, experts and nonexperts, and it will provide a clear and direct path to several topics of current research interest." - Juan J. Font, Mathematical Reviews, Issue 2004jshow more

About James E. Jamison

Central Michigan University, Mount Pleasant, Michigan, USA University of Memphis, Memphis, Tennessee, USAshow more

Table of contents

Preface THE BANACH-STONE PROPERTY Introduction Strictly Convex Spaces and Jerison's Theorem M Summands and Cambern's Theorem Centralizers, Function Modules, and Behrend's Theorem The Nonsurjective Vector-Valued Case The Nonsurjective Case for Nice Operators Notes and Remarks The Banach-Stone Property for Bochner Spaces Introduction LP Functions with Values in Hilbert Space LP Functions with Values in Banach Space L2 Functions with Values in Banach Space Notes and Remarks Orthogonal Decompostions Introduction Sequence Space Decompositions Hermitian Elements and Orthonormal Systems The Case for Real Scalars: Functional Hilbertian Sums Decompositions with Banach Space Factors Notes and Remarks Matrix Spaces Introduction Morita's Proof of Schur's Theorem Isometries for (p, k) Norms on Square Matrix Spaces Isometries for (p, k) Norms on Rectangular Matrix Spaces Notes and Remarks Isometries of Norm Ideals of Operators Introduction Isometries of CP Isometries of Symmetric Norm Ideals: Sourour's Theorem Noncommutative LP Spaces Notes and Remarks Minimal and Maximal Norms Introduction An Infinite-Dimensional Space with Trivial Isometries Minimal Norms Maximal Norms and Forms of Transitivity Notes and Remarks Epilogue Reflexivity of the Isometry Group Adjoint Abelian Operators Almost Isometries Distance One Preserving Maps Spectral Isometries Isometric Equivalence Potpourri BIBLIOGRAPHY INDEXshow more