This project is mathematical research on algebras of operators on Hilbert space. Interest in such algebras grew out of their role in certain formulations of quantum mechanics, operators in the given algebra corresponding more or less to observable quantities in the system being represented. Unlike those customarily encountered in physical models, the algebras in the present study are nonselfadjoint, and so fall into a less well-developed area of the theory. More specifically, the behavior of certain nonselfadjoint operator algebras under tensor products will be investigated in connection with an approximation property for such algebras. Questions concerning hyperreflexivity of operator algebras will be explored. A newly discovered correspondence between finite- dimensional commutative subspace lattice algebras and finite simplicial complexes that takes Hochschild cohomology to simplicial cohomology will be further developed.
