Completely Sidon sets in C∗-algebras

A sequence in a C ∗ -algebra A is called completely Sidon if its span in A is completely isomorphic to the operator space version of the space ℓ 1 (i.e. ℓ 1 equipped with its maximal operator space structure). The latter can also be described as the span of the free unitary generators in the (full)...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Monatshefte für Mathematik 2018-10, Vol.187 (2), p.357-374
1. Verfasser: Pisier, Gilles
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:A sequence in a C ∗ -algebra A is called completely Sidon if its span in A is completely isomorphic to the operator space version of the space ℓ 1 (i.e. ℓ 1 equipped with its maximal operator space structure). The latter can also be described as the span of the free unitary generators in the (full) C ∗ -algebra of the free group F ∞ with countably infinitely many generators. Our main result is a generalization to this context of Drury’s classical theorem stating that Sidon sets are stable under finite unions. In the particular case when A = C ∗ ( G ) the (maximal) C ∗ -algebra of a discrete group G , we recover the non-commutative (operator space) version of Drury’s theorem that we recently proved. We also give several non-commutative generalizations of our recent work on uniformly bounded orthonormal systems to the case of von Neumann algebras equipped with normal faithful tracial states.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-018-1190-y