Remarks on the similarity degree of an operator algebra

Details Remarks on the similarity degree of an operator algebra Remarks on the similarity degree of an operator algebra

2000-09-06

arxiv.org/abs/math/0009052v2

Mathematics

Functional Analysis

Scientific paper

The "similarity" degree of a unital operator algebra $A$ 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 $II_1$ factor with property $\Gamma$ is at most 5, improving on a previous bound ($\le 44$) due to E. Christensen.

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