Resumen de Injective cogenerators among operator bimodules

Bojan Magajna

• Given C*-algebras A and B acting cyclically on Hilbert spaces H and K, respectively, we characterize completely isometric A,B-bimodule maps from B(K,H) into operator A,B-bimodules. We determine cogenerators in some classes of operator bimodules. For an injective cogenerator X in a suitable category of operator A,B-bimodules we show: if A, regarded as a C*-subalgebra of Al(X) (adjointable left multipliers on X), is equal to its relative double commutant in Al(X), then A must be a W*-algebra.