Tame functionals on Banach algebras

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In the present note we introduce tame functionals on Banach algebras. A functional f € A∗ on a Banach algebraA is tame if the naturally defined linear operator A → A∗, a Ü→ f Aa 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 the group algebra l11(G) are induced exactly by tame functions (in the sense of topological dynamics) on G for every discrete group G. That is, Tame(l11(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 languageEnglish
Title of host publicationBanach Algebras and Applications - Proceedings of the International Conference
EditorsMahmoud Filali
PublisherWalter de Gruyter GmbH
Number of pages14
ISBN (Electronic)9783110601329
StatePublished - 26 Oct 2020
Event2017 23rd Conference on Banach Algebras and Applications - Oulu, Finland
Duration: 3 Jul 201711 Jul 2017

Publication series

NameDe Gruyter Proceedings in Mathematics
ISSN (Print)2942-4801
ISSN (Electronic)2942-4828


Conference2017 23rd Conference on Banach Algebras and Applications

Bibliographical note

Publisher Copyright:
© 2020 Walter de Gruyter GmbH, Berlin/Munich/Boston.


  • Asplund space
  • Banach algebra
  • Fragmentability
  • Group algebra
  • Reflexive space
  • Rosenthal dichotomy
  • Rosenthal space
  • Tame functional
  • WAP functional


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