The four investigators will pursue a variety of problems having to do with operators and algebras of operators on Hilbert space. One area of research is multiparameter operator theory, in which such notions as spectrum are considered in joint fashion for tuples of operators rather than for single operators. Another line of investigation concerns differentiable structure on operator algebras, including the study of unbounded derivations and of Lie group actions. Recently discovered connections between knot theory and the theory of operator algebras will be explored. The setting of Hilbert space and the linear operators that transform it is fundamental for representing many of the structures and phenomena encountered in mathematics. Basic features of this setting are infinite-dimensionality, in other words infinitely many degrees of freedom, and noncommutativity, in other words the result of a sequence of operations depends on the order in which the operations are performed. The overall aim of the research in this project is to extend still further the powerful strategy of representing things by operators.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
8801329
Program Officer
William Y. Velez
Project Start
Project End
Budget Start
1988-06-01
Budget End
1992-05-31
Support Year
Fiscal Year
1988
Total Cost
$398,327
Indirect Cost
Name
University of Iowa
Department
Type
DUNS #
City
Iowa City
State
IA
Country
United States
Zip Code
52242