p-Operator space structure on Feichtinger--Figà-Talamanca--Herz Segal algebras

2012/08/10 by Serap Öztop, Öztop, Serap, Nico Spronk +1
Mathematics · #22D12 #43A15 #46J10 #47L25 #47L50 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1208.2072

openalex publication_date 2012/08/10 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28

Abstract

We consider the minimal boundedly-translation-invariant Segal algebra S₀^p(G) in the Figà-Talamanca--Herz algebra A_p(G) of a locally compact group G. In the case that p=2 and G is abelian this is the classical Segal algebra of Feichtinger. Hence we call this the Feichtinger--Figà-Talamanca--Herz Segal algebra of G. Remarkably, this space is also a Segal algebra in L¹(G) and is, in fact, the minimal such algebra which is closed under pointwise multiplication by \apg. Even for p=2, this result is new for non-abelian G. We place a p-operator space structure on S₀^p(G), and demonstrate the naturality of this by showing that it satisfies all natural functiorial properties: projective tensor products, restriction to subgroups and averaging over normal subgroups. However, due to complications arising within the theory of p-operator spaces, we are forced to work with weakly completely bounded maps in many of our results.

Related

• Operator Figa-Talamanca-Herz algebras
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