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Dual Algebras with Applications to Invariant Subspaces and Dilation Theory
Hari Bercovici, Ciprian Foiaş, and Carl Pearcy
A co-publication of the AMS and CBMS.
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CBMS Regional Conference Series in Mathematics
1985; 108 pp; softcover
Number: 56
Reprint/Revision History:
reprinted with corrections 1996
ISBN-10: 0-8218-0706-4
ISBN-13: 978-0-8218-0706-4
List Price: US$28
Member Price: US$22.40
All Individuals: US$22.40
Order Code: CBMS/56
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The theory of dual algebras (ultraweakly closed algebras of operators on Hilbert space) has made tremendous progress since 1978, when Scott Brown originated some of the main ideas to solve the invariant subspace problem for subnormal operators. The impetus for much of this progress has come from the authors of the present book, who, in a sequence of papers, have added several new ideas concerning the solution of systems of simultaneous equations in the predual of a dual algebra, thereby developing a dilation theory and contributing substantially to the theories of invariant subspaces and reflexivity. In addition to containing the major results of the theory as presented in earlier papers by the authors and other mathematicians, this important study presents much material not previously available elsewhere. Accessible to graduate students having knowledge of a first course in operator theory, this excellent book will be of interest to all researchers in the field.

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Table of Contents

  • Dual algebras
  • Simultaneous systems of equations in the predual of a dual algebra
  • The properties \(X_{\theta,\gamma}\) and the properties \((\mathbf A_n)\)
  • Singly generated dual algebras
  • Dilation theory of the class \(\mathbf A_{\aleph_0}\)
  • Sufficient conditions for membership in \(\mathbf A_{\aleph_0}\)
  • Weak density and membership in \(\mathbf A_{\aleph_0}\)
  • The classes (BCP)\(_\theta\) and the functional model of a contractin
  • Invariant subspaces and reflexivity
  • Applications to shifts and subnormal operators
  • References
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