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Local Multipliers of C*-Algebras (Paperback, Softcover reprint of the original 1st ed. 2003)
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Local Multipliers of C*-Algebras (Paperback, Softcover reprint of the original 1st ed. 2003)
Series: Springer Monographs in Mathematics
Expected to ship within 10 - 15 working days
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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).
General
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