Analytic Hilbert Modules

By: Kunyu Guo, Xiaoman Chen

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Hardcover | 26 March 2003 | Edition Number 1

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210 Pages

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23.4 x 15.6 x 1.27

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The seminal 1989 work of Douglas and Paulsen on the theory of Hilbert modules over function algebras precipitated a number of major research efforts. This in turn led to some intriguing and valuable results, particularly in the areas of operator theory and functional analysis. With the field now beginning to blossom, the time has come to collect those results in one volume. Written by two of the most active and often-cited researchers in the field, Analytic Hilbert Modules offers a clear, logical survey of recent developments, including advances made by authors and others. It provides much-needed insight into function theory of several variables and includes significant results published here for the first time in areas such as characteristic space theory, rigidity phenomena, the equivalence problem, Arveson modules, extension theory, and reproducing Hilbert spaces on n-dimensional complex space.

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...I would recommend this book to a researcher who is already familiar with this area and wants to get a good overview of what can be gained from Guo and Chen's methods. It is clear that their methods are valuable and can be used to extend and simplify many results in the area... - Mathematical Reviews

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Introduction	p. 1
Characteristic spaces and algebraic reduction	p. 11
Characteristic spaces for ideals of polynomials	p. 11
Algebraic reduction for analytic Hilbert modules	p. 22
Submodules with finite rank	p. 32
AF-cosubmodules	p. 38
Finite codimensional submodules of Bergman modules	p. 44
Remarks on Chapter 2	p. 48
Rigidity for analytic Hilbert modules	p. 49
Rigidity for analytic Hilbert modules	p. 50
Rigidity for quotient modules	p. 56
Rigidity for Hardy submodules on the polydisk	p. 60
Rigidity for Bergman modules	p. 69
Remarks on Chapter 3	p. 72
Equivalence of Hardy submodules	p. 75
Preliminaries	p. 75
Unitary equivalence of Hardy submodules on the unit polydisk	p. 81
Similarity of Hardy submodules on the unit polydisk	p. 88
Equivalence of Hardy submodules on the unit ball	p. 92
Remarks on Chapter 4	p. 94
Reproducing function spaces on the complex n-space	p. 95
Algebraic reduction for quasi-invariant subspaces	p. 96
Some basic properties of reproducing Hilbert spaces on the complex plane	p. 99
Equivalence of quasi-invariant subspaces on the complex plane	p. 105
Similarity of quasi-invariant subspaces on the complex n-space	p. 111
Quasi-invariant subspaces of the Fock space	p. 112
Finite codimensional quasi-invariant subspaces	p. 121
Beurling's phenomenon on the Fock space	p. 124
Remarks on Chapter 5	p. 126
The Arveson module	p. 127
Some basic results on the Arveson module	p. 127
The Toeplitz algebra on the Arveson space	p. 137
Submodules of the Arveson module	p. 142
Rigidity for Arveson submodules	p. 151
Remarks on Chapter 6	p. 156
Extensions of Hilbert modules	p. 159
The basic theory of extensions	p. 159
Extensions of hypo-Silov modules over unit modulus algebras	p. 163
Extensions of Hilbert modules and Hankel operators	p. 173
Extensions of normal Hilbert module over the ball algebra	p. 180
Remarks on Chapter 7	p. 187
References	p. 189
Index	p. 199
Table of Contents provided by Ingram. All Rights Reserved.

Analytic Hilbert Modules

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Hardcover

Industry Reviews

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