On the Duality of Operator Spaces

摘要

We prove that given an operator space structure on a dual Banach space r, it is not necessarily the dual one of some operator space structure on Y This allows us to show that Sakai's theorem providing the identification between C*-algebras having a predual and von Neumann algebras does not extend to the category of operator spaces We also mclude a related result about completely bounded operators from BU2Y into the operator Hilbert space OH.