Herz-Schur Multipliers and Non-Uniformly Bounded Representations of Locally Compact Groups

Let G be a second countable, locally compact group and let f be a continuous Herz-Schur multiplier on G. Our main result gives the existence of a (not necessarily uniformly bounded) strongly continuous representation on a Hilbert space, such that f is the coefficient of this representation with resp...

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Bibliographic Details
Published in:arXiv.org 2010-01
Main Author: Steenstrup, Troels
Format: Article
Language:English
Subjects:
Hilbert space
Representations
Online Access:Get full text
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Summary:Let G be a second countable, locally compact group and let f be a continuous Herz-Schur multiplier on G. Our main result gives the existence of a (not necessarily uniformly bounded) strongly continuous representation on a Hilbert space, such that f is the coefficient of this representation with respect to two vectors with bounded orbit. Moreover, we show that the norm of the representation of an element g from G is at most exponential in terms of the metric distance from g to the identity element of G.
ISSN:2331-8422