Mathematical Sciences: Problems in Operator Theory and Nonselfadjoint Operator Algebras

点击翻译按钮获取中文摘要

This project is for mathematical research in operator theory. The original impetus for this theory came from a fundamental insight in quantum mechanics, namely that physical quantities normally regarded as scalars are better represented by thinking of them as operators on Hilbert space, where they can interact in a more interesting fashion. The analysis of operators and how they transform the underlying space has since acquired a distinguished existence of its own, apart from physics. More specifically, Professor Bercovici will study a new class of nonselfadjoint operator algebras called dual algebras, with an emphasis on the existence and classification of invariant subspaces. He will enrich the perturbation theory of n-tuples of selfadjoint operators, and will also investigate skew Toeplitz operators. The latter study impinges significantly on control theory issues in engineering.