**CBMS Regional Conference Series in Mathematics**

Volume: 56;
1985;
108 pp;
Softcover

MSC: Primary 47;

Print ISBN: 978-0-8218-0706-4

Product Code: CBMS/56

List Price: $30.00

Individual Price: $24.00

**Electronic ISBN: 978-1-4704-2418-3
Product Code: CBMS/56.E**

List Price: $30.00

Individual Price: $24.00

# Dual Algebras with Applications to Invariant Subspaces and Dilation Theory

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*Hari Bercovici; Ciprian Foiaş; Carl Pearcy*

A co-publication of the AMS and CBMS

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.

#### Table of Contents

# Table of Contents

## Dual Algebras with Applications to Invariant Subspaces and Dilation Theory

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents vii8 free
- Preface ix10 free
- Acknowledgement xi12 free
- I. Dual Algebras 114 free
- II. Simultaneous Systems of Equations in the Predual of a Dual Algebra 720
- III. The Properties X[sub(θ ),(γ)] and the Properties (A[sub(n)] 2134
- IV. Singly Generated Dual Algebras 3346
- V. Dilation Theory of the Class A[sub(ℵ0)] 4356
- VI. Sufficient Conditions for Membership in A[sub(ℵ0)] 5366
- VII. Weak Density and Membership in A[sub(ℵ0)] 6578
- VIII. The Classes (BCP)[sub(θ)] and the Functional Model of a Contraction 7588
- IX. Invariant Subspaces and Reflexivity 89102
- X. Applications to Shifts and Subnormal Operators 101114
- References 107120
- Back Cover Back Cover1123