Tame functionals on Banach algebras

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


Copyright © 2017, arXiv, All rights reserved. In the present note we introduce tame functionals on Banach algebras. A functional f ∈ A∗ on a Banach algebra A is tame if the naturally defined linear operator A → A∗, a 7→ f · a factors through Rosenthal Banach spaces (i.e., not containing a copy of l1). Replacing Rosenthal by reflexive we get a well known concept of weakly almost periodic functionals. So, always WAP(A) ⊆ Tame(A). We show that tame functionals on l1(G) are induced exactly by tame functions (in the sense of topological dynamics) on G for every discrete group G. That is, Tame(l1(G)) = Tame(G). Many interesting tame functions on groups come from dynamical systems theory. Recall that WAP(L1(G)) = WAP(G) (Lau [19], Ülger [28]) for every locally compact group G. It is an open question if Tame(L1(G)) = Tame(G) holds for (nondiscrete) locally compact groups.
Original languageAmerican English
Title of host publicationBanach algebras and applications
Subtitle of host publicationProceedings of the International Conference held at the University of Oulu, July 3-11, 2017
EditorsMahmoud Filali
PublisherDe Gruyter (Berlin, Boston)
Number of pages14
ISBN (Print)9783110602418
StatePublished - 2020

Publication series

NameBanach Algebras and Applications


Dive into the research topics of 'Tame functionals on Banach algebras'. Together they form a unique fingerprint.

Cite this