Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46M35, 46E30, 47B38, 47D15

Retrieve articles in all journals with MSC: 46M35, 46E30, 47B38, 47D15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1081938-1
PII: S 0002-9947(1992)1081938-1
Article copyright: © Copyright 1992 American Mathematical Society