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

2010/01/03 by Troels Steenstrup, Steenstrup, Troels
Mathematics · #22D12 (Primary) 46L07 (Secondary) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #Representation Theory (math.RT) #Spectral Theory in Mathematical Physics #advanced mathematical theories #math.OA #math.RT #msc:22D12 #msc:46L07

paper · pdf · doi:10.48550/arxiv.1001.0326

12 pages

arxiv created 2010/01/03 · openalex publication_date 2010/01/03 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Completely compact Herz-Schur multipliers of dynamical systems
• Factorization and boundedness for representations of locally compact groups on topological vector spaces
• Multipliers and lacunary sets in non-amenable groups
• Are Unitarizable Groups Amenable?
• On the multipliers of the Figa-Talamanca Herz algebra