Representation Theory on Locally Compact Groups

Majumder, Priyanka (2016) Representation Theory on Locally Compact Groups. Masters thesis, Indian Institute of Technology Hyderabad.

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Abstract

In this project we try to reach one of the famous problems, namely similarity problems. Itcan be stated as follows: Is every uniformly bounded continuous representation of locally compact group G is unitarizable? This problem is open for a while until, in 1955, Ehrenpreeis and Mautner gave counterexample for G = SL2(R). In the positive direction, the most general result seems to be Dixmiers theorem which says that if G is amenable then the above problem is affirmative. But the converse remains an open problem. It can be stated as, if all uniformly bounded continuous representations of a group G are uniterizable is G necessarily amenable?

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IITH Creators:
IITH CreatorsORCiD
Item Type: Thesis (Masters)
Uncontrolled Keywords: LCA Groups, Matrix Exponetial, TD506
Subjects: ?? sub3.8 ??
Divisions: Department of Mathematics
Depositing User: Library Staff
Date Deposited: 05 May 2016 05:11
Last Modified: 05 May 2016 05:11
URI: http://raiith.iith.ac.in/id/eprint/2320
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