A superreflexive Banach space which does not admit complex structure

Szarek, Stanisław J.

doi:10.1090/S0002-9939-1986-0840625-5

A superreflexive Banach space which does not admit complex structure
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Proc. Amer. Math. Soc. 97 (1986), 437-444 Request permission

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.

References

Tsirelson superspaces and

94

A complex Banach space such that

and

are not isomorphic

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