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Local Multipliers of C*-Algebras
Tag Description
099$aOnline resource: Springer
100$aAra, Pere.
245$aLocal Multipliers of C*-Algebras$h[EBook] /$cby Pere Ara, Martin Mathieu.
260$aLondon :$bSpringer London :$bImprint: Springer,$c2003.
300$aXII, 319 p.$bonline resource.
338$aonline resource$bcr$2rdacarrier
440$aSpringer Monographs in Mathematics,$x1439-7382
505$a1. 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.
520$aMany problems in operator theory lead to the consideration ofoperator equa­ tions, either directly or via some reformulation. More often than not, how­ ever, the underlying space is too 'small' to contain solutions of these equa­ tions and thus it has to be 'enlarged' in some way. The Berberian-Quigley enlargement of a Banach space, which allows one to convert approximate into genuine eigenvectors, serves as a classical example. In the theory of operator algebras, a C*-algebra A that turns out to be small in this sense tradition­ ally is enlarged to its (universal) enveloping von Neumann algebra A". This works well since von Neumann algebras are in many respects richer and, from the Banach space point of view, A" is nothing other than the second dual space of A. Among the numerous fruitful applications of this principle is the well-known Kadison-Sakai theorem ensuring that every derivation 8 on a C*-algebra A becomes inner in A", though 8 may not be inner in A. The transition from A to A" however is not an algebraic one (and cannot be since it is well known that the property of being a von Neumann algebra cannot be described purely algebraically). Hence, ifthe C*-algebra A is small in an algebraic sense, say simple, it may be inappropriate to move on to A". In such a situation, A is typically enlarged by its multiplier algebra M(A).
538$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700$aMathieu, Martin.$eauthor.
710$aSpringerLink (Online service)
830$aSpringer Monographs in Mathematics,$x1439-7382
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