2010; Physical and Mathematical Sciences, 45(1 (224): 40–43
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NON-UNITARIZABLE GROUPS

H. R. Rostami*

Received: 2025-02-23 · Published: 2010-10-21

© 2010 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
NON-UNITARIZABLE GROUPS
Author
H. R. Rostami
Published
2010-10-21
Licence
Creative Commons Attribution 4.0 International

Abstract

A group G is called unitarizable, if every uniformly bounded representation π:G→B(H) of G on a Hilbert space H is unitarizable. N. Monod and N. Ozawa in [6] prove that free Burnside groups B(m,n) are non unitarizable for arbitrary composite odd number n=n1n2 , where n1≥665 . We prove that for the same n the groups B(4,n) have continuum many non-isomorphic factor-groups, each one of which is non-unitarizable and uniformly non-amenable.
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