Operator Theory/Operator Algebras

Operator Theory and Operator Algebras are concerned with the study of linear operators, usually on vector spaces whose elements are functions. The subject is analysis, but because the vector spaces are usually infinite dimensional, the subject has a nice blend of techniques from other areas of mathematics, ranging from algebra to topology to dynamical systems.


Allan Donsig's research interests are in Operator Theory and Operator Algebras, in particular, structural results for nonselfadjoint operator algebras. Recent papers are on such topics as coordinatization results, the structure of analytic partial crossed products, and the norms of Schur matrices. More information, including recent papers, are on Allan's homepage.

Adam Fuller's research is in Operator Theory and Operator Algebras. In particular Adam works on dilation theory of representations, semicrossed product algebras and the nonself-adjoint algebras arising from graphs and k-graphs.

John Orr does work in Operator Theory mostly on the ideals of non-selfadjoint algebras. He has published papers on the algebraic structure of nest algebras, CSL algebras, and triangular algebras.

David Pitts has interests in coordinatization of operator algebras, operator space theory, free semigroup algebras (a non-commutative analog of analytic functions in several variables) and nest algebras.

Gordon Woodward has mathematical interests in classical harmonic analysis and wavelets.

Graduate Students

Philip Gipson David Pitts

Jeremy Parrott David Pitts

Travis Russell Allan Donsig

Christopher Schafhauser Allan Donsig and David Pitts