Geometric spects A of Similarity Problems

This article presents a geometric approach to some similarity problems involving metric arguments in the non-positively curved space of positive invertible operators of an operator algebra and the canonical isometric action by invertible elements on the cone given by g . a = gag*. Through this approach, we extend and put into a geometric framework results by Pisier and partially answer a question by Andruchow et al. about minimality properties of canonical unitarizers.