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Mathematics Colloquium

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Date:  Tuesday, October 09, 2012

Title:  Homogeneous operators: a class of Hilbert space operators relarted to representation theory and holomorphy

Abstract:  Homogeneous operators.

A bounded operator T on a Hilbert space is called homogeneous if its spectrum
is contained in the closed unit disc D and if, for every g in the Mobius group (the
holomorphic automorphism group of D), g(T) is unitarily equivalent to T. In the last
twenty years several people studied this class. This talk will begin with the discussion of
examples and some basic properties such as the existence of a projective representation
of the Mobius group associated to T, and the fact that T is a so-called block shift. Then
it will proceed to two recent results. One, joint with G. Misra, is the classification and
description of all homogeneous operators in the so-called Cowen-Douglas class. The
other is the description of a new family of examples (not in the Cowen-Douglas class).


Speaker:  Adam Koranyi
Institution:  CUNY, Graduate Center, and Lehman College

 

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