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Quasi-multipliers of operator spaces. (English) Zbl 1067.46050

Summary: We use the injective envelope to study quasi-multipliers of operator spaces. We prove that all representable operator algebra products that an operator space can be endowed with are induced by quasi-multipliers. We obtain generalizations of the Banach-Stone theorem.

MSC:

46L07 Operator spaces and completely bounded maps
46L05 General theory of \(C^*\)-algebras
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
47A20 Dilations, extensions, compressions of linear operators
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References:

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