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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A Banach couple is determined
by the collection of its interpolation spaces


Authors: O. E. Tikhonov and L. V. Veselova
Journal: Proc. Amer. Math. Soc. 126 (1998), 1049-1054
MSC (1991): Primary 46B70; Secondary 46M35
MathSciNet review: 1443170
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that an arbitrary Banach couple is uniquely determined by the collection of all its interpolation spaces, which extends a result by N. Aronszajn and E. Gagliardo.


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

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Additional Information

O. E. Tikhonov
Affiliation: Research Institute of Mathematics and Mechanics, Kazan State University, Universitetskaya Str. 17, Kazan, Tatarstan, 420008 Russia
Email: Oleg.Tikhonov@ksu.ru

L. V. Veselova
Affiliation: Department of Higher Mathematics, Kazan State Technological University, Karl Marx Str. 68, Kazan, Tatarstan, 420015 Russia

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04209-9
PII: S 0002-9939(98)04209-9
Keywords: Banach couple, interpolation space
Received by editor(s): November 7, 1995
Received by editor(s) in revised form: September 23, 1996
Additional Notes: Supported by the Russian Foundation for Basic Research, grant no.\ 95–01–00025.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society