Softcover ISBN:  9780821807064 
Product Code:  CBMS/56 
List Price:  $34.00 
Individual Price:  $27.20 
eBook ISBN:  9781470424183 
Product Code:  CBMS/56.E 
List Price:  $32.00 
Individual Price:  $25.60 
Softcover ISBN:  9780821807064 
eBook: ISBN:  9781470424183 
Product Code:  CBMS/56.B 
List Price:  $66.00 $50.00 
Softcover ISBN:  9780821807064 
Product Code:  CBMS/56 
List Price:  $34.00 
Individual Price:  $27.20 
eBook ISBN:  9781470424183 
Product Code:  CBMS/56.E 
List Price:  $32.00 
Individual Price:  $25.60 
Softcover ISBN:  9780821807064 
eBook ISBN:  9781470424183 
Product Code:  CBMS/56.B 
List Price:  $66.00 $50.00 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 56; 1985; 108 ppMSC: Primary 47
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.
Readership 
Table of Contents

Chapters

I. Dual Algebras

II. Simultaneous Systems of Equations in the Predual of a Dual Algebra

III. The Properties $X_{\theta , \gamma }$ and the Properties $(\mathbb {A}_n)$

IV. Singly Generated Dual Algebras

V. Dilation Theory of the Class $\mathbb {A}_{N_0}$

VI. Sufficient Conditions for Membership in $\mathbb {A}_{N_0}$

VII. Weak Density and Membership in $\mathbb {A}_{N_0}$

VIII. The Classes (BCP)$_{\theta }$ and the Functional Model of a Contraction

IX. Invariant Subspaces and Reflexivity

X. Applications to Shifts and Subnormal Operators


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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.

Chapters

I. Dual Algebras

II. Simultaneous Systems of Equations in the Predual of a Dual Algebra

III. The Properties $X_{\theta , \gamma }$ and the Properties $(\mathbb {A}_n)$

IV. Singly Generated Dual Algebras

V. Dilation Theory of the Class $\mathbb {A}_{N_0}$

VI. Sufficient Conditions for Membership in $\mathbb {A}_{N_0}$

VII. Weak Density and Membership in $\mathbb {A}_{N_0}$

VIII. The Classes (BCP)$_{\theta }$ and the Functional Model of a Contraction

IX. Invariant Subspaces and Reflexivity

X. Applications to Shifts and Subnormal Operators