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Hardcover ISBN:  9780821815366 
Product Code:  SURV/36 
List Price:  $139.00 
MAA Member Price:  $125.10 
AMS Member Price:  $111.20 
eBook ISBN:  9781470412630 
Product Code:  SURV/36.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Hardcover ISBN:  9780821815366 
eBook ISBN:  9781470412630 
Product Code:  SURV/36.B 
List Price:  $274.00 $206.50 
MAA Member Price:  $246.60 $185.85 
AMS Member Price:  $219.20 $165.20 

Book DetailsMathematical Surveys and MonographsVolume: 36; 1991; 436 ppMSC: Primary 47; Secondary 32; 46
“In a certain sense, subnormal operators were introduced too soon because the theory of function algebras and rational approximation was also in its infancy and could not be properly used to examine this class of operators. The progress in the theory of subnormal operators that has come about during the last several years grew out of applying the results of rational approximation.”
—from the Preface
This book is the successor to the author's 1981 book on the same subject. In addition to reflecting the great strides in the development of subnormal operator theory since the first book, the present work is oriented toward rational functions rather than polynomials. Although the book is a research monograph, it has many of the traits of a textbook, including exercises.
The book requires background in function theory and functional analysis, but is otherwise fairly selfcontained. The first few chapters cover the basics about subnormal operator theory and present a study of analytic functions on the unit disk. Other topics included are: some results on hyponormal operators, an exposition of rational approximation interspersed with applications to operator theory, a study of weakstar rational approximation, a set of results that can be termed structure theorems for subnormal operators, and a proof that analytic bounded point evaluations exist.

Table of Contents

Chapters

I. Preliminaries

II. Subnormal operators: The elementary theory

III. Function theory on the unit circle

IV. Hyponormal operators

V. Uniform rational approximation

VI. Weakstar rational approximation

VII. Some structure theory for subnormal operators

VIII. Bounded point evaluations


Reviews

As we have come to expect of the author, the standard of exposition is extremely high.
Bulletin of the London Mathematical Society 
The authors pedagogical, almost conversational style makes this book a pleasure to read; even experts in subnormal operator theory will want this book as a reference ... the author has developed in this text the theory of subnormal operators with clarity and humor. Anyone interested in operator theory or related areas of functional analysis will find this book a valuable reference.
Mathematical Reviews


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“In a certain sense, subnormal operators were introduced too soon because the theory of function algebras and rational approximation was also in its infancy and could not be properly used to examine this class of operators. The progress in the theory of subnormal operators that has come about during the last several years grew out of applying the results of rational approximation.”
—from the Preface
This book is the successor to the author's 1981 book on the same subject. In addition to reflecting the great strides in the development of subnormal operator theory since the first book, the present work is oriented toward rational functions rather than polynomials. Although the book is a research monograph, it has many of the traits of a textbook, including exercises.
The book requires background in function theory and functional analysis, but is otherwise fairly selfcontained. The first few chapters cover the basics about subnormal operator theory and present a study of analytic functions on the unit disk. Other topics included are: some results on hyponormal operators, an exposition of rational approximation interspersed with applications to operator theory, a study of weakstar rational approximation, a set of results that can be termed structure theorems for subnormal operators, and a proof that analytic bounded point evaluations exist.

Chapters

I. Preliminaries

II. Subnormal operators: The elementary theory

III. Function theory on the unit circle

IV. Hyponormal operators

V. Uniform rational approximation

VI. Weakstar rational approximation

VII. Some structure theory for subnormal operators

VIII. Bounded point evaluations

As we have come to expect of the author, the standard of exposition is extremely high.
Bulletin of the London Mathematical Society 
The authors pedagogical, almost conversational style makes this book a pleasure to read; even experts in subnormal operator theory will want this book as a reference ... the author has developed in this text the theory of subnormal operators with clarity and humor. Anyone interested in operator theory or related areas of functional analysis will find this book a valuable reference.
Mathematical Reviews