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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.
List of contents
1. Path Spaces, Continuous Tensor Products, and E0-Semigroups.- 2. Some General Theory of Operator Algebras and their Modules.- 3. Polynomially Bounded Operators, a Survey.- 4. Operator Analogues of Locally Convex Spaces.- 5. Basis Theory and Operator Algebras.- 6. Reflexivity, Supports and Spectral Synthesis.- 7. Geometric Aspects of the theory of Nest Algebras.- 8. Finitely-presented C*-algebras.- 9. von Neumann Algebras and Wavelets.- 10. A Finite Dimensional Introduction to Operator Algebra.- 11. The Pythagoreans: From Harmony to the Irrational.- 12. Relative Yoneda Cohomology for Operator Spaces: an Overview.- 13. Partly Self-adjoint Limit Algebras.- 14. Operator Algebras over C* -correspondences.- 15. Conditional Expectations and Projection Maps of von Neuman Algebras.
