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Fellows Directory

John Ringrose

Professor John Ringrose FRS

Fellow


Elected: 1977

Biography

John Ringrose has made major contributions to the theory of algebras of operators on Hilbert spaces, especially in long-standing collaboration with Richard V. Kadison. They showed that certain von Neumann algebras have only inner derivations — a result extended by Shoichiro Sakai to all von Neumann algebras and to some other C*-algebras. John and Richard also developed the fundamental properties of the automorphism group of a C*-algebra, as a topological group with the uniform topology.

Of particular note is their theorem that every automorphism at distance less than 2 from the identity is the exponential of a derivation and so lies on a norm-continuous, one-parameter subgroup, and is implemented by a unitary operator in the von Neumann closure in every representation. In addition, they laid the foundations of a cohomology theory for C*-algebras.

John has worked also on the triangular representation of compact linear operators (especially those in the Schmidt class), and has initiated a study of nests of subspaces and the corresponding triangular operator algebras, or ‘nest algebras’.

Professional positions

Emeritus Professor of Pure Mathematics, Newcastle University, Physics Department

Interests and expertise

Subject groups

Keywords

C*-algebras, Hilbert space, nest algebras, von Neumann algebras