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A superreflexive banach spaceX withL(X) admitting a homomorphism onto the Banach algebraC(βN)

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Abstract

A separable superreflexive Banach spaceX is constructed such that the Banach algebraL(X) of all continuous endomorphisms ofX admits a continuous homomorphism onto the Banach algebraC(βN) of all scalar valued functions on the Stone-Čech compacification of the positive integers with supremum norm. In particular: (i) the cardinality of the set of all linear multiplicative functionals onL(X) is equal to 2c and (ii)X is not isomorphic to any finite Cartesian power of any Banach space.

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Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland

    P. Mankiewicz

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  1. P. Mankiewicz
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Mankiewicz, P. A superreflexive banach spaceX withL(X) admitting a homomorphism onto the Banach algebraC(βN). Israel J. Math. 65, 1–16 (1989). https://doi.org/10.1007/BF02788171

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  • DOI: https://doi.org/10.1007/BF02788171

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