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Inhaltsangabe
Many problems in operator theory lead to the consideration ofoperator equa tions, either directly or via some reformulation. More often than not, how ever, the underlying space is too 'small' to contain solutions of these equa tions and thus it has to be 'enlarged' in some way. The Berberian-Quigley enlargement of a Banach space, which allows one to convert approximate into genuine eigenvectors, serves as a classical example. In the theory of operator algebras, a C*-algebra A that turns out to be small in this sense tradition ally is enlarged to its (universal) enveloping von Neumann algebra A". This works well since von Neumann algebras are in many respects richer and, from the Banach space point of view, A" is nothing other than the second dual space of A. Among the numerous fruitful applications of this principle is the well-known Kadison-Sakai theorem ensuring that every derivation 8 on a C*-algebra A becomes inner in A", though 8 may not be inner in A. The transition from A to A" however is not an algebraic one (and cannot be since it is well known that the property of being a von Neumann algebra cannot be described purely algebraically). Hence, ifthe C*-algebra A is small in an algebraic sense, say simple, it may be inappropriate to move on to A". In such a situation, A is typically enlarged by its multiplier algebra M(A).
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Many problems in operator theory lead to the consideration ofoperator equa tions, either directly or via some reformulation. More often than not, how ever, the underlying space is too 'small' to contain solutions of these equa tions and thus it has to be 'enlarged' in some way. The Berberian-Quigley enlargement of a Banach space, which allows one to convert approximate into genuine eigenvectors, serves as a classical example. In the theory of operator algebras, a C*-algebra A that turns out to be small in this sense tradition ally is enlarged to its (universal) enveloping von Neumann algebra A". This works well since von Neumann algebras are in many respects richer and, from the Banach space point of view, A" is nothing other than the second dual space of A. Among the numerous fruitful applications of this principle is the well-known Kadison-Sakai theorem ensuring that every derivation 8 on a C*-algebra A becomes inner in A", though 8 may not be inner in A. The transition from A to A" however is not an algebraic one (and cannot be since it is well known that the property of being a von Neumann algebra cannot be described purely algebraically). Hence, ifthe C*-algebra A is small in an algebraic sense, say simple, it may be inappropriate to move on to A". In such a situation, A is typically enlarged by its multiplier algebra M(A).
Reseña del editor
The theme of this book is operator theory on C*-algebras. The main novel tool employed is the concept of local multipliers. Originally devised by Elliott and Pedersen in the 1970's in order to study derivations and automorphisms, local multipliers of C*-algebras were developed into a powerful device by the present authors in the 1990's. The book serves two purposes. The first part provides the reader - specialist and advanced graduate student alike - with a thorough introduction to the theory of local multipliers. Only a minimal knowledge of algebra and analysis is required, as the prerequisites in both non-commutative ring theory and basic C*-algebra theory are presented in the first chapter. In the second part, local multipliers are used to obtain a wealth of information on various classes of operators on C*-algebras, including (groups of) automorphisms, derivations, elementary operators, Lie isomorphisms and Lie derivations, as well as others. Many of the results appear in print for the first time. The authors have made an effort to avoid intricate technicalities thus some of the results are not pushed to their utmost generality. Several open problems are discussed, and hints for further developments are given.
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Local Multipliers of C*-Algebras
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Local multipliers of C*-algebras.
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Local Multipliers of C*-Algebras
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Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. No other book on C*-algebra covers local multipliers of C*-algebras This book includes applications that have not yet appeared in print, from respected experts in the fieldNo other book on C*-algebra covers local multipliers of C*-algeb. Bestandsnummer des Verkäufers 4289428
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Local Multipliers of C*-Algebras
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Springer London, Springer London Okt 2002, 2002
ISBN 10: 1852332379
ISBN 13: 9781852332372
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Buch. Zustand: Neu. Neuware -Many problems in operator theory lead to the consideration ofoperator equa tions, either directly or via some reformulation. More often than not, how ever, the underlying space is too 'small' to contain solutions of these equa tions and thus it has to be 'enlarged' in some way. The Berberian-Quigley enlargement of a Banach space, which allows one to convert approximate into genuine eigenvectors, serves as a classical example. In the theory of operator algebras, a C\*-algebra A that turns out to be small in this sense tradition ally is enlarged to its (universal) enveloping von Neumann algebra A'. This works well since von Neumann algebras are in many respects richer and, from the Banach space point of view, A' is nothing other than the second dual space of A. Among the numerous fruitful applications of this principle is the well-known Kadison-Sakai theorem ensuring that every derivation 8 on a C\*-algebra A becomes inner in A', though 8 may not be inner in A. The transition from A to A' however is not an algebraic one (and cannot be since it is well known that the property of being a von Neumann algebra cannot be described purely algebraically). Hence, ifthe C\*-algebra A is small in an algebraic sense, say simple, it may be inappropriate to move on to A'. In such a situation, A is typically enlarged by its multiplier algebra M(A).Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 340 pp. Englisch. Bestandsnummer des Verkäufers 9781852332372
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Local Multipliers of C\*-Algebras
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Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Many problems in operator theory lead to the consideration ofoperator equa tions, either directly or via some reformulation. More often than not, how ever, the underlying space is too 'small' to contain solutions of these equa tions and thus it has to be 'enlarged' in some way. The Berberian-Quigley enlargement of a Banach space, which allows one to convert approximate into genuine eigenvectors, serves as a classical example. In the theory of operator algebras, a C\*-algebra A that turns out to be small in this sense tradition ally is enlarged to its (universal) enveloping von Neumann algebra A'. This works well since von Neumann algebras are in many respects richer and, from the Banach space point of view, A' is nothing other than the second dual space of A. Among the numerous fruitful applications of this principle is the well-known Kadison-Sakai theorem ensuring that every derivation 8 on a C\*-algebra A becomes inner in A', though 8 may not be inner in A. The transition from A to A' however is not an algebraic one (and cannot be since it is well known that the property of being a von Neumann algebra cannot be described purely algebraically). Hence, ifthe C\*-algebra A is small in an algebraic sense, say simple, it may be inappropriate to move on to A'. In such a situation, A is typically enlarged by its multiplier algebra M(A). 340 pp. Englisch. Bestandsnummer des Verkäufers 9781852332372
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Local Multipliers of C*-Algebras
Verlag:
Springer London, Springer London, 2002
ISBN 10: 1852332379
ISBN 13: 9781852332372
Neu
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - Many problems in operator theory lead to the consideration ofoperator equa tions, either directly or via some reformulation. More often than not, how ever, the underlying space is too 'small' to contain solutions of these equa tions and thus it has to be 'enlarged' in some way. The Berberian-Quigley enlargement of a Banach space, which allows one to convert approximate into genuine eigenvectors, serves as a classical example. In the theory of operator algebras, a C\*-algebra A that turns out to be small in this sense tradition ally is enlarged to its (universal) enveloping von Neumann algebra A'. This works well since von Neumann algebras are in many respects richer and, from the Banach space point of view, A' is nothing other than the second dual space of A. Among the numerous fruitful applications of this principle is the well-known Kadison-Sakai theorem ensuring that every derivation 8 on a C\*-algebra A becomes inner in A', though 8 may not be inner in A. The transition from A to A' however is not an algebraic one (and cannot be since it is well known that the property of being a von Neumann algebra cannot be described purely algebraically). Hence, ifthe C\*-algebra A is small in an algebraic sense, say simple, it may be inappropriate to move on to A'. In such a situation, A is typically enlarged by its multiplier algebra M(A). Bestandsnummer des Verkäufers 9781852332372
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Local Multipliers of C*-Algebras
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