On the range of completely bounded maps

Richard I. Loebl

International Journal of Mathematics and Mathematical Sciences, 1978, vol. 1, 1-7

Abstract:

It is shown that if every bounded linear map from a C * -algebra α to a von Neumann algebra β is completely bounded, then either α is finite-dimensional or β ⫅ 𝒞 ⊗ M n , where 𝒞 is a commutative von Neumann algebra and M n is the algebra of n × n complex matrices.

Date: 1978
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:619759

DOI: 10.1155/S0161171278000241

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