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.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
8802417
Program Officer
William Y. Velez
Project Start
Project End
Budget Start
1988-06-01
Budget End
1991-11-30
Support Year
Fiscal Year
1988
Total Cost
$43,858
Indirect Cost
Name
Indiana University
Department
Type
DUNS #
City
Bloomington
State
IN
Country
United States
Zip Code
47401