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 "LP"("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 isometrieson 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.
General
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