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Operator Algebras and Applications
During the last few years, the theory of operator algebras, particularly non-self-adjoint operator algebras, has evolved dramatically, experiencing both international growth and interfacing with other important areas. The present volume presents a survey of some of the latest developments in the field in a form that is detailed enough to be accessible to advanced graduate students as well as researchers in the field. Among the topics treated are: operator spaces, Hilbert modules, limit algebras, reflexive algebras and subspaces, relations to basis theory, C* algebraic quantum groups, endomorphisms of operator algebras, conditional expectations and projection maps, and applications, particularly to wavelet theory. The volume also features an historical paper offering a new approach to the Pythagoreans' discovery of irrational numbers.
Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations
This volume contains a selection of papers, from experts in the area, on multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations. Operator Theory, Systems Theory and Scattering Theory will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Nonselfadjoint Operator Algebras, Operator Theory, and Related Topics
This volume, dedicated to Carl Pearcy on the occasion of his 60th birthday, presents recent results in operator theory, nonselfadjoint operator algebras, measure theory and the theory of moments. The articles on these subjects have been contributed by leading area experts, many of whom were associated with Carl Pearcy as students or collaborators. The book testifies to his multifaceted interests and includes a biographical sketch and a list of publications.
Algebraic Methods in Operator Theory
The theory of operators stands at the intersection of the frontiers of modern analysis and its classical counterparts; of algebra and quantum mechanics; of spectral theory and partial differential equations; of the modern global approach to topology and geometry; of representation theory and harmonic analysis; and of dynamical systems and mathematical physics. The present collection of papers represents contributions to a conference, and they have been carefully selected with a view to bridging different but related areas of mathematics which have only recently displayed an unexpected network of interconnections, as well as new and exciting cross-fertilizations. Our unify ing theme is the al...
Completely Positive Hypergroup Actions
It is now well know that the measure algebra [script capital]M([italic capital]G) of a locally compact group can be regarded as a subalgebra of the operator algebra [italic capital]B([italic capital]B([italic capital]L2([italic capital]G))) of the operator algebra [italic capital]B([italic capital]L2([italic capital]G)) of the Hilbert space [italic capital]L2([italic capital]G). We study the situation in hypergroups and find that, in general, the analogous map for them is neither an isometry nor a homomorphism. However, it is completely positive and completely bounded in certain ways. This work presents the related general theory and special examples.
On Finite Groups and Homotopy Theory
In part 1 we study the homology, homotopy, and stable homotopy of [capital Greek]Omega[italic capital]B[lowercase Greek]Pi[up arrowhead][over][subscript italic]p, where [italic capital]G is a finite [italic]p-perfect group. In part 2 we define the concept of resolutions by fibrations over an arbitrary family of spaces.
Advances in Quantum Dynamics
This volume contains the proceedings of the conference on Advances in Quantum Dynamics. The purpose of the conference was to assess the current state of knowledge and to outline future research directions of quantum dynamical semigroups on von Neumann algebras. Since the appearance of the landmark papers by F. Murray and J. von Neumann, On the Rings of Operators, von Neumann algebras have been used as a mathematical model in the study of time evolution of quantum mechanical systems.Following the work of M. H. Stone, von Neumann, and others on the structure of one-parameter groups of unitary transformations, many researchers have made fundamental contributions to the understanding of time-rev...
Stratifying Endomorphism Algebras
This paper presents a systematic study of the relationships between the representation theories of [italic capital]R and [italic capital]A, especially those involving actual or potential quasi-hereditary structures on the latter algebra. Our original motivation comes from the theory of Schur algebras, work of Soergel on the Bernstein-Gelfand-Gelfand category [script capital]O, and resent results of Dlab-Heath-Marko realizing certain endomorphism algebras as quasi-hereditary algebras. We synthesize common features of all these examples, and go beyond them in a number of new directions.
Reductive Subgroups of Exceptional Algebraic Groups
The theory of simple algebraic groups is important in many areas of mathematics. The authors of this book investigate the subgroups of certain types of simple algebraic groups and obtain a complete description of all those subgroups which are themselves simple. This description is particularly useful in understanding centralizers of subgroups and restrictions of representations.
Integrable Systems and Riemann Surfaces of Infinite Genus
This memoir develops the spectral theory of the Lax operators of nonlinear Schrödinger-like partial differential equations with periodic boundary conditions. Their special curves, i.e., the common spectrum with the periodic shifts, are generically Riemann surfaces of infinite genus. The points corresponding to infinite energy are added. The resulting spaces are no longer Riemann surfaces in the usual sense, but they are quite similar to compact Riemann surfaces.
