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A superreflexive Banach space which does not admit complex structure


Author: Stanisław J. Szarek
Journal: Proc. Amer. Math. Soc. 97 (1986), 437-444
MSC: Primary 46B10; Secondary 46B20
DOI: https://doi.org/10.1090/S0002-9939-1986-0840625-5
MathSciNet review: 840625
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Abstract: We construct an infinite-dimensional superreflexive real Banach space which does not admit complex structure and consequently is not isomorphic to the Cartesian square of any Banach space. We also construct a variant of Bourgain's example of a complex Banach space with nonunique complex structure and state a number of open problems about structure of Banach spaces and their linear groups.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0840625-5
Article copyright: © Copyright 1986 American Mathematical Society

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