A twisted inclusion between tensor products of operator spaces

Abstract

Given operator spaces V and W , let W denote the opposite operator space structure on the same underlying Banach space. Although the identity map W → W is in general not completely bounded, we show that the identity map on V ⊗W extends to a contractive linear map V ⊗ W → V ⊗ min W , where ⊗ and ⊗ min denote the projective and injective tensor products of operator spaces. We then sketch how this aids us in constructing anti-symmetric 2-cocycles on certain Fourier algebras.Dedicated to John Rainwater, with thanks for his varied contributions and generous spirit.