Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces

by L. Molnár

Overview

The territory of preserver problems has grown continuously within linear analysis. This book presents a cross-section of the modern theory of preservers on infinite dimensional spaces (operator spaces and function spaces) through the author's corresponding results. Special emphasis is placed on preserver problems concerning some structures of Hilbert space operators which appear in quantum mechanics. In addition, local automorphisms and local isometries of operator algebras and function algebras are discussed in detail.

Product Details

ISBN-13:	9783540399445
Publisher:	Springer Berlin Heidelberg
Publication date:	11/16/2006
Series:	Lecture Notes in Mathematics , #1895
Edition description:	2007
Pages:	236
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Some Linear and Multiplicative Preserver Problems on Operator Algebras and Function Algebras.- Preservers on Quantum Structures.- Local Automorphisms and Local Isometries of Operator Algebras and Function Algebras.

Editorial Reviews

From the reviews:

"Preserver problems deal with maps on subsets of algebras that preserve certain sets, relations, functions, etc. … The book is very well organized. … One of its remarkable features is that it links several areas, particularly operator theory and mathematical physics. The audience of this book is therefore potentially wide: operator algebraists, mathematical physicists, linear algebraists, ring theorists, etc. I warmly recommend this book to anyone interested in preserver problems." (Matej Brešar, Mathematical Reviews, Issue, 2007 g)

"The monograph under review collects many important and highly nontrivial results and efforts. It is important to recall that the basic material is based on the research done by the author, who belongs to the eminent researchers in this field. The style is very fresh … . I recommend to book for students and experts interested in operator algebra, noncommutative measure theory and mathematical foundations of quantum physics. The monograph is welcome in the quantum structures realm." (Anatolij Dvurecenskij, Zentralblatt MATH, Vol. 1119 (21), 2007)

From the Publisher