eBook ISBN:  9780821894309 
Product Code:  PSPUM/51.2.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9780821894309 
Product Code:  PSPUM/51.2.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 

Book DetailsProceedings of Symposia in Pure MathematicsVolume: 51; 1990; 385 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

Gregory T. Adams — Reduced Hankel operators and radial measures [ MR 1077414 ]

E. A. Azoff and H. A. Shehada — From algebras of normal operators to intersecting hyperplanes [ MR 1077415 ]

B. M. Baker and D. E. Handelman — Random walks, $K_0$theory for AF algebras, and classical statistical mechanics [ MR 1077416 ]

K. Berman, H. Halpern, V. Kaftal and G. Weiss — Some $C_4$ and $C_6$ norm inequalities related to the paving problem [ MR 1077417 ]

Paul S. Bourdon and Joel H. Shapiro — Cyclic composition operators on $H^2$ [ MR 1077418 ]

Robert P. Boyer — Representation theory of $\mathrm {U}(\infty )$ [ MR 1077419 ]

Chris Brislawn — Trace class integral kernels [ MR 1077420 ]

Geon H. Choe — Products of operators with singular continuous spectra [ MR 1077421 ]

Raúl E. Curto — Joint hyponormality: a bridge between hyponormality and subnormality [ MR 1077422 ]

Alexander Dynin — Algebras generated by classical pseudodifferential operators on open Riemannian manifolds [ MR 1077423 ]

C. K. Fong, E. A. Nordgren, H. Radjavi and P. Rosenthal — A similarity invariant [ MR 1077424 ]

Jeffrey Fox, Peter Haskell and William Pardon — Two themes in index theory on singular varieties [ MR 1077425 ]

Ichiro Fujimoto — $\mathrm {CP}$duality for $C^*$ and $W^*$algebras [ MR 1077426 ]

Frank Gilfeather — A note on special CSL algebras with nontrivial cohomology [ MR 1077427 ]

Elliot C. Gootman and Aldo J. Lazar — Actions of compact groups on $C^*$algebras [ MR 1077428 ]

William L. Green and T. D. Morley — Parallel sums of operators [ MR 1077429 ]

J. J. Grobler — The zerotwo law and the peripheral spectrum of positive contractions in Banach lattice algebras [ MR 1077430 ]

Herbert Halpern, Victor Kaftal and László Zsidó — Finite weight projections in von Neumann factors [ MR 1077431 ]

Ronghui Ji — Toeplitz operators on noncommutative tori and their real valued index [ MR 1077432 ]

Mahmood Khoshkam — Close $C^*$algebras are $KK$equivalent [ MR 1077433 ]

Edward V. Kissin — On derivations of operator algebras implemented by bounded operators [ MR 1077434 ]

Thomas L. Kriete, III and Barbara D. MacCluer — Composition operators and weighted polynomial approximation [ MR 1077435 ]

Alan Lambert — Seminormality for measuretheoretic composition operators [ MR 1077436 ]

David R. Larson and Ahmed R. Sourour — Local derivations and local automorphisms of $\mathcal {B}(X)$ [ MR 1077437 ]

Martin Mathieu — How to use primeness to describe properties of elementary operators [ MR 1077438 ]

Brian W. McEnnis — Shifts on Krein spaces [ MR 1077439 ]

James A. Mingo — Inner completely positive maps on von Neumann algebras [ MR 1077440 ]

R. L. Moore and T. T. Trent — Isometries of nest algebras [ MR 1077441 ]

Hitoshi Moriyoshi — Chern character for proper $\Gamma $manifolds [ MR 1077442 ]

Michihiro Nagase and Tomio Umeda — Selfadjointness of quantum Hamiltonians of relativistic and nonrelativistic particles in electromagnetic fields [ MR 1077443 ]

C. Peligrad — Actions of compact groups on $C^*$algebras [ MR 1077444 ]

Justin R. Peters and Yiu Tung Poon — Invariants for triangular $\mathrm {AF}$ algebras [ MR 1077445 ]

N. Christopher Phillips — $K$theory and noncommutative homotopy theory [ MR 1077446 ]

R. J. Plymen — Equivalence bimodules in the representation theory of reductive groups [ MR 1077447 ]

Mihai Putinar — Spectral theory and sheaf theory. IV [ MR 1077448 ]

Leiba Rodman — On factorization of selfadjoint operator polynomials [ MR 1077449 ]

Claude Schochet — The Kasparov groups for commutative $C^*$algebras and SpanierWhitehead duality [ MR 1077450 ]

Albert JeuLiang Sheu — How are the Toeplitz $C^*$algebras of Reinhardt domains affected by taking pseudoconvex hulls? [ MR 1077451 ]

John S. Spielberg — Factor state extensions on $O_2$ [ MR 1077452 ]

Silviu Teleman — On the DaunsHofmann theorem [ MR 1077453 ]

T. T. Trent and W. Wogen — Subnormal operators with a common invariant subspace [ MR 1077454 ]

Martin E. Walter — $C^*$algebras and the classification of finite groups [ MR 1077455 ]

Xiaolu Wang — Bivariant Chern character I [ MR 1077456 ]

Warren R. Wogen — Composition operators acting on spaces of holomorphic functions on domains in $\mathbf {C}^n$ [ MR 1077457 ]

Ke Ren Yan — Rigidity theorem and Buerling theorem [ MR 1077458 ]

Ke He Zhu — On certain unitary operators and composition operators [ MR 1077459 ]


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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

Gregory T. Adams — Reduced Hankel operators and radial measures [ MR 1077414 ]

E. A. Azoff and H. A. Shehada — From algebras of normal operators to intersecting hyperplanes [ MR 1077415 ]

B. M. Baker and D. E. Handelman — Random walks, $K_0$theory for AF algebras, and classical statistical mechanics [ MR 1077416 ]

K. Berman, H. Halpern, V. Kaftal and G. Weiss — Some $C_4$ and $C_6$ norm inequalities related to the paving problem [ MR 1077417 ]

Paul S. Bourdon and Joel H. Shapiro — Cyclic composition operators on $H^2$ [ MR 1077418 ]

Robert P. Boyer — Representation theory of $\mathrm {U}(\infty )$ [ MR 1077419 ]

Chris Brislawn — Trace class integral kernels [ MR 1077420 ]

Geon H. Choe — Products of operators with singular continuous spectra [ MR 1077421 ]

Raúl E. Curto — Joint hyponormality: a bridge between hyponormality and subnormality [ MR 1077422 ]

Alexander Dynin — Algebras generated by classical pseudodifferential operators on open Riemannian manifolds [ MR 1077423 ]

C. K. Fong, E. A. Nordgren, H. Radjavi and P. Rosenthal — A similarity invariant [ MR 1077424 ]

Jeffrey Fox, Peter Haskell and William Pardon — Two themes in index theory on singular varieties [ MR 1077425 ]

Ichiro Fujimoto — $\mathrm {CP}$duality for $C^*$ and $W^*$algebras [ MR 1077426 ]

Frank Gilfeather — A note on special CSL algebras with nontrivial cohomology [ MR 1077427 ]

Elliot C. Gootman and Aldo J. Lazar — Actions of compact groups on $C^*$algebras [ MR 1077428 ]

William L. Green and T. D. Morley — Parallel sums of operators [ MR 1077429 ]

J. J. Grobler — The zerotwo law and the peripheral spectrum of positive contractions in Banach lattice algebras [ MR 1077430 ]

Herbert Halpern, Victor Kaftal and László Zsidó — Finite weight projections in von Neumann factors [ MR 1077431 ]

Ronghui Ji — Toeplitz operators on noncommutative tori and their real valued index [ MR 1077432 ]

Mahmood Khoshkam — Close $C^*$algebras are $KK$equivalent [ MR 1077433 ]

Edward V. Kissin — On derivations of operator algebras implemented by bounded operators [ MR 1077434 ]

Thomas L. Kriete, III and Barbara D. MacCluer — Composition operators and weighted polynomial approximation [ MR 1077435 ]

Alan Lambert — Seminormality for measuretheoretic composition operators [ MR 1077436 ]

David R. Larson and Ahmed R. Sourour — Local derivations and local automorphisms of $\mathcal {B}(X)$ [ MR 1077437 ]

Martin Mathieu — How to use primeness to describe properties of elementary operators [ MR 1077438 ]

Brian W. McEnnis — Shifts on Krein spaces [ MR 1077439 ]

James A. Mingo — Inner completely positive maps on von Neumann algebras [ MR 1077440 ]

R. L. Moore and T. T. Trent — Isometries of nest algebras [ MR 1077441 ]

Hitoshi Moriyoshi — Chern character for proper $\Gamma $manifolds [ MR 1077442 ]

Michihiro Nagase and Tomio Umeda — Selfadjointness of quantum Hamiltonians of relativistic and nonrelativistic particles in electromagnetic fields [ MR 1077443 ]

C. Peligrad — Actions of compact groups on $C^*$algebras [ MR 1077444 ]

Justin R. Peters and Yiu Tung Poon — Invariants for triangular $\mathrm {AF}$ algebras [ MR 1077445 ]

N. Christopher Phillips — $K$theory and noncommutative homotopy theory [ MR 1077446 ]

R. J. Plymen — Equivalence bimodules in the representation theory of reductive groups [ MR 1077447 ]

Mihai Putinar — Spectral theory and sheaf theory. IV [ MR 1077448 ]

Leiba Rodman — On factorization of selfadjoint operator polynomials [ MR 1077449 ]

Claude Schochet — The Kasparov groups for commutative $C^*$algebras and SpanierWhitehead duality [ MR 1077450 ]

Albert JeuLiang Sheu — How are the Toeplitz $C^*$algebras of Reinhardt domains affected by taking pseudoconvex hulls? [ MR 1077451 ]

John S. Spielberg — Factor state extensions on $O_2$ [ MR 1077452 ]

Silviu Teleman — On the DaunsHofmann theorem [ MR 1077453 ]

T. T. Trent and W. Wogen — Subnormal operators with a common invariant subspace [ MR 1077454 ]

Martin E. Walter — $C^*$algebras and the classification of finite groups [ MR 1077455 ]

Xiaolu Wang — Bivariant Chern character I [ MR 1077456 ]

Warren R. Wogen — Composition operators acting on spaces of holomorphic functions on domains in $\mathbf {C}^n$ [ MR 1077457 ]

Ke Ren Yan — Rigidity theorem and Buerling theorem [ MR 1077458 ]

Ke He Zhu — On certain unitary operators and composition operators [ MR 1077459 ]