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Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry

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When is the multiplication map bounded? [duplicate]

Forgive me if my question is too elementary however I haven't found this issue discussed anywhere. Suppose that $A$ is arbitrary $C^*$-algebra and consider the multiplication map $A \overline{\otimes} …
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