Miglioli, MartinSchlicht, Peter2019-01-312019-01-312019-01-312018-12-0110.1093/imrn/rnx102https://infoscience.epfl.ch/handle/20.500.14299/154243WOS:000456063600003This 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.Mathematicsuniformly bounded representationstheoremtext::journal::journal article::research article