eBook ISBN:  9780821894293 
Product Code:  PSPUM/51.1.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9780821894293 
Product Code:  PSPUM/51.1.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 

Book DetailsProceedings of Symposia in Pure MathematicsVolume: 51; 1990; 640 ppMSC: Primary 47; Secondary 00; 46
Operator theory has come of age during the last twenty years. The subject has developed in several directions using new and powerful methods that have led to the solution of basic problems previously thought to be inaccessible. In addition, operator theory has had fundamental connections with a range of other mathematical topics. For example, operator theory has made mutually enriching contacts with other areas of mathematics, such as algebraic topology and index theory, complex analysis, and probability theory. The algebraic methods employed in operator theory are diverse and touch upon a broad area of mathematics. There have been direct applications of operator theory to systems theory and statistical mechanics. And significant problems and motivations have arisen from the subject's traditional underpinnings for partial differential equations.
This twovolume set contains the proceedings of an AMS Summer Institute on Operator Theory/Operator Algebras, held in July 1988 at the University of New Hampshire. The Institute sought to summarize progress and examine the common points of view that now run through the subject. With contributions from some of the top experts in the field, this publication illuminates a broad range of current research topics in operator theory.
This item is also available as part of a set: 
Table of Contents

Articles

William Arveson — The spectral $C^*$algebra of an $E_0$semigroup [ MR 1077377 ]

Joseph A. Ball, Israel Gohberg and Leiba Rodman — Twosided LagrangeSylvester interpolation problems for rational matrix functions [ MR 1077378 ]

Asher BenArtzi and Israel Gohberg — Nonstationary inertia theorems, dichotomy, and applications [ MR 1077379 ]

L. A. Coburn — Toeplitz operators, quantum mechanics, and mean oscillation in the Bergman metric [ MR 1077380 ]

John B. Conway — Towards a functional calculus for subnormal tuples: the minimal normal extension and approximation in several complex variables [ MR 1077381 ]

H. O. Cordes — On the technique of comparison algebra for elliptic boundary problems on noncompact manifolds [ MR 1077382 ]

Carl C. Cowen — Composition operators on Hilbert spaces of analytic functions: a status report [ MR 1077383 ]

Raúl E. Curto, Paul S. Muhly and Jingbo Xia — Random Toeplitz operators [ MR 1077384 ]

Kenneth R. Davidson — Isomorphisms of nest algebras and their quotients [ MR 1077385 ]

R. G. Douglas — Invariants for Hilbert modules [ MR 1077386 ]

Edward G. Effros and ZhongJin Ruan — Multivariable multipliers for groups and their operator algebras [ MR 1077387 ]

J. William Helton — Beyond commutant lifting [ MR 1077388 ]

Domingo A. Herrero — Similarity and approximation of operators [ MR 1077389 ]

Nigel Higson — A primer on $KK$theory [ MR 1077390 ]

Alan Hopenwasser — Complete distributivity [ MR 1077391 ]

Jerome Kaminker — Operator algebraic invariants for elliptic operators [ MR 1077392 ]

Abel Klein — The supersymmetric replica trick and smoothness of the density of states for random Schrödinger operators [ MR 1077393 ]

David R. Larson — Some recent progress in nest algebras [ MR 1077394 ]

Vern I. Paulsen — Rigidity theorems in spaces of analytic functions [ MR 1077395 ]

Vladimir V. Peller — Hankel operators and multivariate stationary processes [ MR 1077396 ]

Joel Pincus — The principal index [ MR 1077397 ]

S. C. Power — Refinement theory for nonselfadjoint operator algebras [ MR 1077398 ]

Robert T. Powers — Some remarks on the index theory for semigroups of $*$endomorphisms of $\mathfrak {B}(\mathfrak {H})$ [ MR 1077399 ]

Marc A. Rieffel — Deformation quantization and operator algebras [ MR 1077400 ]

Richard Rochberg — Toeplitz and Hankel operators, wavelets, NWO sequences, and almost diagonalization of operators [ MR 1077401 ]

Jonathan Rosenberg — $K$ and $KK$: topology and operator algebras [ MR 1077402 ]

Norberto Salinas — Applications of $C^*$algebras and operator theory to proper holomorphic mappings [ MR 1077403 ]

Donald Sarason — Function theory and de Branges’s spaces [ MR 1077404 ]

Irving Segal — Algebraic quantization and stability [ MR 1077405 ]

Baruch Solel — Analytic operator algebras [ MR 1077406 ]

Uffe Haagerup and Erling Størmer — Automorphisms which preserve unitary equivalence classes of normal states [ MR 1077407 ]

Masamichi Takesaki — Cocycle conjugacy of group actions on factors [ MR 1077408 ]

Michael E. Taylor — Pseudodifferential operators and $K$homology [ MR 1077409 ]

Harald Upmeier — Toeplitz operators and index theory in several complex variables [ MR 1077410 ]

Harold Widom — Szegő expansions for operators with smooth or nonsmooth symbol [ MR 1077411 ]

Daoxing Xia — Analytic theory of a subnormal $n$tuple of operators [ MR 1077412 ]


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Operator theory has come of age during the last twenty years. The subject has developed in several directions using new and powerful methods that have led to the solution of basic problems previously thought to be inaccessible. In addition, operator theory has had fundamental connections with a range of other mathematical topics. For example, operator theory has made mutually enriching contacts with other areas of mathematics, such as algebraic topology and index theory, complex analysis, and probability theory. The algebraic methods employed in operator theory are diverse and touch upon a broad area of mathematics. There have been direct applications of operator theory to systems theory and statistical mechanics. And significant problems and motivations have arisen from the subject's traditional underpinnings for partial differential equations.
This twovolume set contains the proceedings of an AMS Summer Institute on Operator Theory/Operator Algebras, held in July 1988 at the University of New Hampshire. The Institute sought to summarize progress and examine the common points of view that now run through the subject. With contributions from some of the top experts in the field, this publication illuminates a broad range of current research topics in operator theory.

Articles

William Arveson — The spectral $C^*$algebra of an $E_0$semigroup [ MR 1077377 ]

Joseph A. Ball, Israel Gohberg and Leiba Rodman — Twosided LagrangeSylvester interpolation problems for rational matrix functions [ MR 1077378 ]

Asher BenArtzi and Israel Gohberg — Nonstationary inertia theorems, dichotomy, and applications [ MR 1077379 ]

L. A. Coburn — Toeplitz operators, quantum mechanics, and mean oscillation in the Bergman metric [ MR 1077380 ]

John B. Conway — Towards a functional calculus for subnormal tuples: the minimal normal extension and approximation in several complex variables [ MR 1077381 ]

H. O. Cordes — On the technique of comparison algebra for elliptic boundary problems on noncompact manifolds [ MR 1077382 ]

Carl C. Cowen — Composition operators on Hilbert spaces of analytic functions: a status report [ MR 1077383 ]

Raúl E. Curto, Paul S. Muhly and Jingbo Xia — Random Toeplitz operators [ MR 1077384 ]

Kenneth R. Davidson — Isomorphisms of nest algebras and their quotients [ MR 1077385 ]

R. G. Douglas — Invariants for Hilbert modules [ MR 1077386 ]

Edward G. Effros and ZhongJin Ruan — Multivariable multipliers for groups and their operator algebras [ MR 1077387 ]

J. William Helton — Beyond commutant lifting [ MR 1077388 ]

Domingo A. Herrero — Similarity and approximation of operators [ MR 1077389 ]

Nigel Higson — A primer on $KK$theory [ MR 1077390 ]

Alan Hopenwasser — Complete distributivity [ MR 1077391 ]

Jerome Kaminker — Operator algebraic invariants for elliptic operators [ MR 1077392 ]

Abel Klein — The supersymmetric replica trick and smoothness of the density of states for random Schrödinger operators [ MR 1077393 ]

David R. Larson — Some recent progress in nest algebras [ MR 1077394 ]

Vern I. Paulsen — Rigidity theorems in spaces of analytic functions [ MR 1077395 ]

Vladimir V. Peller — Hankel operators and multivariate stationary processes [ MR 1077396 ]

Joel Pincus — The principal index [ MR 1077397 ]

S. C. Power — Refinement theory for nonselfadjoint operator algebras [ MR 1077398 ]

Robert T. Powers — Some remarks on the index theory for semigroups of $*$endomorphisms of $\mathfrak {B}(\mathfrak {H})$ [ MR 1077399 ]

Marc A. Rieffel — Deformation quantization and operator algebras [ MR 1077400 ]

Richard Rochberg — Toeplitz and Hankel operators, wavelets, NWO sequences, and almost diagonalization of operators [ MR 1077401 ]

Jonathan Rosenberg — $K$ and $KK$: topology and operator algebras [ MR 1077402 ]

Norberto Salinas — Applications of $C^*$algebras and operator theory to proper holomorphic mappings [ MR 1077403 ]

Donald Sarason — Function theory and de Branges’s spaces [ MR 1077404 ]

Irving Segal — Algebraic quantization and stability [ MR 1077405 ]

Baruch Solel — Analytic operator algebras [ MR 1077406 ]

Uffe Haagerup and Erling Størmer — Automorphisms which preserve unitary equivalence classes of normal states [ MR 1077407 ]

Masamichi Takesaki — Cocycle conjugacy of group actions on factors [ MR 1077408 ]

Michael E. Taylor — Pseudodifferential operators and $K$homology [ MR 1077409 ]

Harald Upmeier — Toeplitz operators and index theory in several complex variables [ MR 1077410 ]

Harold Widom — Szegő expansions for operators with smooth or nonsmooth symbol [ MR 1077411 ]

Daoxing Xia — Analytic theory of a subnormal $n$tuple of operators [ MR 1077412 ]