Operator Theory Seminar (309 VAN) - Peter Burton, PhD; Iowa State University

Apr 25, 2023

01:30 PM - 02:30 PM

Van Allen Hall, 309

30 North Dubuque Street, Iowa City, IA 52242

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Peter Burton, Ph.D.; Iowa State University

Intertwining operators between unitary representations of the free group

Peter Burton, PhD; Iowa State University

We consider the question of how to extend an operator connecting two "partial unitary" representations of a discrete group to an intertwining operator between complete unitary representations of the same group. We focus on representations of nonabelian free groups, and our main result is that in this case it is always possible to conduct this extension procedure without increasing the norm of the intertwining operator. Our proceeds by studying positive definite functions and analyzing so-called noncommutative Szego parameters. The work presented is joint with Kate Juschenko.

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