Remarks on the similarity degree of an operator algebra
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 II1 factor with property is at most 5, improving on a previous bound ( 44) due to E. Christensen.
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