Mathematical Sciences: Structural Properties of Non Self Adjoint Operator Algebras

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Orr and Pitts will study the structure of nonselfadjoint operator algebras. In particular, they propose to classify all closed two-sided ideals in continuous nest algebras. Understanding these ideals is likely to lead to new constructions and techniques with triangular operator algebras. Additionally, Pitts proposes to find conditions weaker than hyperreflexivity which ensure that a CSL is stable, and Orr proposes to study ideal structure of CSL algebras and new maximal triangular algebras. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. Operators can be thought of as finite or infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. These seemingly abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA.