Summary
In this chapter, we introduce the space B (G) of coefficients of unitary representations on a discrete group G and a related space T p (G), (1 ≤ p < ∞) of complex valued functions on G. We show that if G = IF N , the free group on N ≥ 2 generators, there are non-unitarizable uniformly bounded representations on G. We give several related characterizations of amenable groups. Then we extend the method to the case of semi-groups. This allows us to produce (this time for G = IN) examples of power bounded operators which are not polynomially bounded.
Keywords
- Unitary Representation
- Toeplitz Oper
- Discrete Group
- Amenable Group
- Hankel Operator
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© 1996 Springer-Verlag Berlin Heidelberg
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Pisier, G. (1996). Non-unitarizable uniformly bounded group representations. In: Similarity Problems and Completely Bounded Maps. Lecture Notes in Mathematics, vol 1618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21537-1_3
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DOI: https://doi.org/10.1007/978-3-662-21537-1_3
Publisher Name: Springer, Berlin, Heidelberg
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