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.