Proceedings of the NATO Advanced Study Institute, `Aegean Conference on Operator Algebras and Applications', Pythagorio, Samos, Greece, August 19-28, 1996

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. Front Matter....Pages i-xi Path Spaces, Continuous Tensor Products, and E 0 -Semigroups....Pages 1-111 Some General Theory of Operator Algebras and Their Modules....Pages 113-143 Polynomially Bounded Operators, A Survey....Pages 145-162 Operator Analogues of Locally Convex Spaces....Pages 163-207 Basis Theory and Operator Algebras....Pages 209-223 Reflexivity, Supports and Spectral Synthesis....Pages 225-243 Geometric Aspects of the Theory of Nest Algebras....Pages 245-254 Finitely-Presented C *-Algebras....Pages 255-266 Von Neumann Algebras and Wavelets....Pages 267-312 A Finite Dimensional Introduction to Operator Algebra....Pages 313-354 The Pythagoreans: From Harmony to the Irrational....Pages 355-387 Relative Yoneda Cohomology for Operator Spaces: an Overview....Pages 389-401 Partly Self-Adjoint Limit Algebras....Pages 403-428 Operator Algebras Over C *-Correspondences....Pages 429-448 Conditional Expectations and Projection Maps of von Neumann Algebras....Pages 449-461 Back Matter....Pages 463-467 Proceedings of the NATO Advanced Study Institute, `Aegean Conference on Operator Algebras and Applications', Pythagorio, Samos, Greece, August 19-28, 1996