The Banach Algebra L¹(G) and Tame Functionals

2023/01/28 by Komisarchik, Matan
#43A20 #43A60 #46A17 #46H05 #54Hxx #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2301.12298

Abstract

We give an affirmative answer to a question due to M. Megrelishvili, and show that for every locally compact group G we have Tame(L¹(G)) = Tame(G), which means that a functional is tame over L¹(G) if and only if it is tame as a function over G. In fact, it is proven that for every norm-saturated, convex vector bornology on RUC_b(G), being small as a function and as a functional is the same. This proves that Asp(L¹(G)) = Asp(G) and reaffirms a well-known, similar result which states that WAP(G) = WAP(L¹(G)).

Related

• Tame functionals on Banach algebras
• Tameness and Rosenthal type locally convex spaces
• Representations of dynamical systems on Banach spaces not containing l₁
• The BSE-property for vector-valued L^p-algebras
• L₁- Properties of vector-valued Banach algebras