Remarks on the similarity degree of an operator algebra

Gilles Pisier

Remarks on the similarity degree of an operator algebra

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arxiv math/0009052 v2 pith:AXG3MX7X submitted 2000-09-06 math.FA math.OA

Gilles Pisier This is my paper · ORCID

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keywords algebradegreelengthoperatorknownseveralsimilaritybound

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abstract

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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