A01=James E. Jamison
A01=Richard J. Fleming
advanced mathematical symmetries
Algebra Isomorphism
Author_James E. Jamison
Author_Richard J. Fleming
Banach Algebras
Banach Space
bergman
Bergman Spaces
Bloch Space
Borel Set
canonical isometry characterization in mathematics
Category=PBKF
Conformal Automorphism
Cozero Set
decomposition
disk
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
functional analysis
Hermitian Operator
homeomorphism applications
isometry
Jordan Triple Product
linear
Linear Isometry
Luxemburg Norm
Measure Spaces
metric space theory
Musielak Orlicz Spaces
normed
open
Open Unit Disk
operator theory methods
Orlicz Norm
Orlicz Spaces
Partial Isometry
rearrangement invariant function spaces
Semi-inner Product
surjective
Surjective Isometry
Triple System
unit
Unit Ball
Von Neumann Algebra
Weighted Composition Operator
wold
Young's Function
Young’s Function
Product details
- ISBN 9781584880400
- Weight: 540g
- Dimensions: 156 x 234mm
- Publication Date: 23 Dec 2002
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric space must transform a continuous function x into a continuous function y satisfying y(t) = h(t)x(p(t)), where p is a homeomorphism and |h| is identically one.
Isometries on Banach Spaces: Function Spaces is the first of two planned volumes that survey investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form given above in a variety of settings. After an introductory discussion of isometries in general, four chapters are devoted to describing the isometries on classical function spaces. The final chapter explores isometries on Banach algebras.
This treatment provides a clear account of historically important results, exposes the principal methods of attack, and includes some results that are more recent and some that are lesser known. Unique in its focus, this book will prove useful for experts as well as beginners in the field and for those who simply want to acquaint themselves with this area of Banach space theory.
Fleming, Richard J.; Jamison, James E.
