Injective Cogenerators among Operator Bimodules
نویسنده
چکیده
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 Csubalgebra 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.
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