Injective cogenerators among operator bimodules

• Autores: Bojan Magajna
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 4, 2007, págs. 1091-1115
• Idioma: inglés
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• Resumen

  • 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.