This project is mathematical research in operator theory, a subject that generalizes to infinite dimensions the basic ideas of linear algebra. The growth of this subject was stimulated by, and has applications to, the study of integral and differential equations, quantum mechanics, and control theory. Many of the specific objectives concern reflexive operator algebras, that is, the algebras of operators that are determined by their invariant subspaces. An infinite-dimensional analogue of triangular form for matrices will be explored. Additional topics for research include operator-theoretic generalizations of the Stone - Weierstrass theorem, invariant operator ranges, weak resolvents, and positive maps of C*-algebras.
