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)...
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Veröffentlicht in: | Monatshefte für Mathematik 2018-10, Vol.187 (2), p.357-374 |
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Format: | Artikel |
Sprache: | eng |
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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. |
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ISSN: | 0026-9255 1436-5081 |
DOI: | 10.1007/s00605-018-1190-y |