English

Remarks on the similarity degree of an operator algebra

Functional Analysis 2007-05-23 v2 Operator Algebras

Abstract

The "similarity" degree of a unital operator algebra AA was defined and studied in two recent papers of ours, where in particular we showed that it coincides with the "length" of an operator algebra. This paper brings several complements: we give direct proofs (with slight improvements) of several known facts on the length which were only known via the degree, and we show that the length of a type II1II_1 factor with property Γ\Gamma is at most 5, improving on a previous bound (44\le 44) due to E. Christensen.

Keywords

Cite

@article{arxiv.math/0009052,
  title  = {Remarks on the similarity degree of an operator algebra},
  author = {Gilles Pisier},
  journal= {arXiv preprint arXiv:math/0009052},
  year   = {2007}
}