The most prominent among them is freeness or free probability, which was introduced by Voiculescu to study questions in

operator algebra theory.

Originally published in Japanese for a Surveys in Geometry workshop held in Tokyo, Japan, in 1998, this translation offers an overview of

operator algebra theory.

Most of the book can be read with only a basic knowledge of functional analysis; however, some experience in the theory of

operator algebra is helpful.

Objective: This project aims to an innovative deep interplay between

Operator Algebras and Quantum Field Theory.

He presents the theory of Krichever-Nobikov algebras, Lax

operator algebras, their interaction, elements of their representation theory, relations to moduli spaces of Riemann surface and holomorphic vector bundles of them and to Lax integrable systems and conformal field theory.

Other topics of the 17 papers include nonself-adjoint

operator algebras for dynamical systems, noncommutative geometry as a functor, examples of mases in C*-algebras, simple group graded rings, and classifying monotone complete algebras of operators.

This time it was decided to expand the scope by including some further topics related to interpolation, such as inequalities, invariant theory, symmetric spaces,

operator algebras, multilinear algebra and division algebras, operator monotonicity and convexity, functional spaces and applications and connections of these topics to nonlinear partial differential equations, geometry, mathematical physics, and economics.

Characterizing linear maps on

operator algebras is one of the most active and fertile research topics in the theory of

operator algebras during the past one hundred years.

Fillmore, A User's guide to

operator algebras, Willey-Interscience, 1996.

Ringrose, Fundamentals of the Theory of

Operator Algebras, Elementary Theory, New York, 1983.

He made a connection between

operator algebras and knot theory," says Birman, whose work on "braids" provided an important link.

Objective: The project lies at the intersection of

operator algebras, operator theory and dynamical systems, with elements of experimental mathematics and applications to noncommutative structures, completely positive dynamics, spectral analysis of functional operators, and potentially to the theory of functional-differential equations and quantum physics.