Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Differentials of complex interpolation processes for Köthe function spaces

Author: N. J. Kalton
Journal: Trans. Amer. Math. Soc. 333 (1992), 479-529
MSC: Primary 46M35; Secondary 46E30, 47B38, 47D15
MathSciNet review: 1081938
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Abstract: We continue the study of centralizers on Köthe function spaces and the commutator estimates they generate (see [29]). Our main result is that if $ X$ is a super-reflexive Köthe function space then for every real centralizer $ \Omega $ on $ X$ there is a complex interpolation scale of Köthe function spaces through $ X$ inducing $ \Omega $ as a derivative, up to equivalence and a scalar multiple. Thus, in a loose sense, all real centralizers can be identified with derivatives of complex interpolation processes. We apply our ideas in an appendix to show, for example, that there is a twisted sum of two Hilbert spaces which fails to be a $ ({\text{UMD}})$-space.

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Article copyright: © Copyright 1992 American Mathematical Society