@inbook{fd02f3b973ad43c59e2118b33c092344,

title = "Tame functionals on Banach algebras",

abstract = "Copyright {\textcopyright} 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], {\"U}lger [28]) for every locally compact group G. It is an open question if Tame(L1(G)) = Tame(G) holds for (nondiscrete) locally compact groups.",

author = "Michael Megrelishvili",

year = "2020",

doi = "10.1515/9783110602418-013",

language = "American English",

isbn = "9783110602418",

series = "Banach Algebras and Applications",

publisher = "De Gruyter (Berlin, Boston)",

pages = "213--226",

editor = "Filali, {Mahmoud }",

booktitle = "Banach algebras and applications",

}