Mathematical Sciences: Operator Algebras

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Operator algebras is a central discipline in Modern Analysis which has important historical and current applications. It arose in the early decades of this century in connection with establishing a mathematical framework for quantum mechanics. This pioneering work, associated with the names of von Neumann and Murray, and referred to as the noncommutative analog of probability theory and of measure theory, treated selfadjoint algebras of operators. In recent years, again in connection with applications in physics as well as in engineering and operator theory, mathematicians have turned their attention to the theory of non-selfadjoint operator algebras. This study is in its infancy, and the structure theory of such algebras is being intensively investigated. Professor Pitts is a young mathematical analyst whose research career is off to a stunning start. He recently completed his doctoral dissertation on the structure of certain types of non-selfadjoint operator algebras called nest algebras, studying them as subalgebras of von Neumann (selfadjoint) algebras. In this work he obtained several new results on factorization problems and connections with K- theory of these algebras. In the current proposal, Professor Pitts plans to continue his successful research activity by investigating difficult and long outstanding problems concerning similarity and connectedness questions in nest algebras.