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Over the past several decades, the territory of preserver problems has been continuously enlarging within the frame of linear analysis. The aim of this work is to present a sort of 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 put on preserver problems concerning some structures of Hilbert space operators which appear in quantum mechanics. Moreover, local automorphisms and local isometries of operator algebras and function algebras are discussed in details.
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 Bresar, 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)
"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 Bresar, 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)