Ebook: Local Multipliers of C*-Algebras
- Tags: Algebra, Operator Theory, Functional Analysis
- Series: Springer Monographs in Mathematics
- Year: 2003
- Publisher: Springer-Verlag London
- Edition: 1
- Language: English
- pdf
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).
Content:
Front Matter....Pages i-xii
Introduction....Pages 1-6
Prerequisites....Pages 7-48
The Symmetric Algebra of Quotients and its Bounded Analogue....Pages 49-70
The Centre of the Local Multiplier Algebra....Pages 71-95
Automorphisms and Derivations....Pages 97-168
Elementary Operators and Completely Bounded Mappings....Pages 169-235
Lie Mappings and Related Operators....Pages 237-295
Back Matter....Pages 297-319
Content:
Front Matter....Pages i-xii
Introduction....Pages 1-6
Prerequisites....Pages 7-48
The Symmetric Algebra of Quotients and its Bounded Analogue....Pages 49-70
The Centre of the Local Multiplier Algebra....Pages 71-95
Automorphisms and Derivations....Pages 97-168
Elementary Operators and Completely Bounded Mappings....Pages 169-235
Lie Mappings and Related Operators....Pages 237-295
Back Matter....Pages 297-319
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