Local Multipliers of C*Algebras [electronic resource] /
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 BerberianQuigley 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 wellknown KadisonSakai 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).
Main Authors:  , , 

Format:  Texto biblioteca 
Language:  eng 
Published: 
London : Springer London : Imprint: Springer,
2003

Subjects:  Mathematics., Algebra., Functional analysis., Operator theory., Operator Theory., Functional Analysis., 
Online Access:  http://dx.doi.org/10.1007/9781447100454 
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