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Local Multipliers of C*-Algebras

Local Multipliers of C*-Algebras
Catalogue Information
Field name Details
Dewey Class 512
Title Local Multipliers of C*-Algebras ([EBook] /) / by Pere Ara, Martin Mathieu.
Author Ara, Pere
Added Personal Name Mathieu, Martin author.
Other name(s) SpringerLink (Online service)
Publication London : : Springer London : : Imprint: Springer, , 2003.
Physical Details XII, 319 p. : online resource.
Series Springer monographs in mathematics 1439-7382
ISBN 9781447100454
Summary Note 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).:
Contents note 1. Prerequisites -- 2. The Symmetric Algebra of Quotients and its Bounded Analogue -- 3. The Centre of the Local Multiplier Algebra -- 4. Automorphisms and Derivations -- 5. Elementary Operators and Completely Bounded Mappings -- 6. Lie Mappings and Related Operators -- References.
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