John R. Ringrose

Bio: John R. Ringrose is an academic researcher from University of Newcastle. The author has contributed to research in topics: Nest algebra & Jordan algebra. The author has an hindex of 11, co-authored 21 publications receiving 3974 citations. Previous affiliations of John R. Ringrose include Newcastle University.

Fundamentals of the Theory of Operator Algebras

Abstract: Comparison theory of projections--exercises and solutions Normal states and unitary equivalence of von Neumann algebras--exercises and solutions The trace--exercises and solutions Algebra and commutant--exercises and solutions Special representations of $C^*$-algebras--exercises and solutions Tensor products--exercises and solutions Approximation by matrix algebras--exercises and solutions Crossed products--exercises and solutions Direct integrals and decomposiitons--exercises and solutions Bibliography Index.

Derivations and automorphisms of operator algebras

Abstract: The theorem that each derivation of aC*-algebra\(\mathfrak{A}\) extends to an inner derivation of the weak-operator closure ϕ(\(\mathfrak{A}\))− of\(\mathfrak{A}\) in each faithful representation ϕ of\(\mathfrak{A}\) is proved in sketch and used to study the automorphism group of\(\mathfrak{A}\) in its norm topology. It is proved that the connected component of the identity i in this group contains the open ball ℬ of radius 2 with centerl and that each automorphism in ℬ extends to an inner automorphism of ϕ(\(\mathfrak{A}\))−.

Quantum information and computation

Abstract: In information processing, as in physics, our classical world view provides an incomplete approximation to an underlying quantum reality. Quantum effects like interference and entanglement play no direct role in conventional information processing, but they can--in principle now, but probably eventually in practice--be harnessed to break codes, create unbreakable codes, and speed up otherwise intractable computations.

Classification of injective factors

Abstract: The fundamental results of A. Connes which determine a complete set of isomorphism classes for most injectlve factors are discussed in detail. After some introductory remarks which lay the foundation for the subsequent discussion, an historical survey of some of the principal lines of the investigation in the classification of factors is presented, culminating in the Connes-Takesakl structure theory of type III factors. After a discussion of inJectlvity for finite factors, the main result of the paper, the uniqueness of the injectlve II 1 factor, is deduced, and the structure of II. and type III injectlve factors is then obtained as corollaries of the main result. 1980 AMS (MOS) SUBJECT CLASSIFICATION: PRIMARY 46L35, 46LI0; SECONDARY- 46L50, 46L05 KEY WORI)S AND PHRASES: jiVe yon Nann o.%gebra, fi facr, dcre

Operator Algebras: Theory of C*-Algebras and von Neumann Algebras

Abstract: Operators on Hilbert Space.- C*-Algebras.- Von Neumann Algebras.- Further Structure.- K-Theory and Finiteness.