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Springer Monographs in Mathematics

Local Multipliers of C*-Algebras

Authors: Ara, Pere, Mathieu, Martin

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About this book

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).

Table of contents (7 chapters)

  • Introduction

    Ara, Pere (et al.)

    Pages 1-6

  • Prerequisites

    Ara, Pere (et al.)

    Pages 7-48

  • The Symmetric Algebra of Quotients and its Bounded Analogue

    Ara, Pere (et al.)

    Pages 49-70

  • The Centre of the Local Multiplier Algebra

    Ara, Pere (et al.)

    Pages 71-95

  • Automorphisms and Derivations

    Ara, Pere (et al.)

    Pages 97-168

Buy this book

eBook £72.00
price for United Kingdom (gross)
  • ISBN 978-1-4471-0045-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover £90.00
price for United Kingdom (gross)
  • ISBN 978-1-85233-237-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover £90.00
price for United Kingdom (gross)
  • ISBN 978-1-4471-1068-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Local Multipliers of C*-Algebras
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2003
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-4471-0045-4
DOI
10.1007/978-1-4471-0045-4
Hardcover ISBN
978-1-85233-237-2
Softcover ISBN
978-1-4471-1068-2
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XII, 319
Topics