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A Banach couple is determined by the collection of its interpolation spaces
Author(s):
O.
E.
Tikhonov;
L.
V.
Veselova
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1049-1054.
MSC (1991):
Primary 46B70;
Secondary 46M35
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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:
- 1.
- N. Aronszajn and E. Gagliardo, Interpolation spaces and interpolation methods, Ann. Mat. Pure ed Appl. 68 (1965), 51-117. MR 37:1951
- 2.
- Yu. A. Brudnyi and N. Ya. Kruglyak, Interpolation functors and interpolation spaces I, North-Holland, 1991. MR 93b:46141
- 3.
- Yu. A. Brudnyi, S. G. Krein, and E. M. Semenov, Interpolation of linear operators, in ``Itogi Nauki i Tekhniki. Matem. Analiz'' 24, Moscow, 1986, pp. 3-163 (Russian); English transl., J. of Soviet Math. 42 (1988), 2009-2113. MR 88e:46056
- 4.
- S. G. Krein, Yu. I. Petunin, and E. M. Semenov, Interpolation of linear operators, ``Nauka'', Moscow, 1978 (Russian); English transl., Amer. Math. Soc., Providence, 1982. MR 84j:46103
- 5.
- L. V. Veselova and O. E. Tikhonov, The uniqueness of the solution to inverse interpolation problems, Research Institute of Mathematics and Mechanics, Preprint no. 95-2, Kazan Mathematics Foundation, Kazan, 1995 (Russian).
- 6.
- O. E. Tikhonov and L. V. Veselova, The uniqueness of the solution to the inverse problem of exact interpolation (submitted to the Proceedings of the International Workshop on Function Spaces, Interpolation Spaces and Related Topics).
- 7.
- L. V. Veselova and O. E. Tikhonov, On the uniqueness of the solution of the inverse exact interpolation problem, Funktsional'nyi Analiz i ego Prilozheniya 26 (2) (1992), 67-68 (Russian); English transl., Funct. Anal. Appl. 26 (2) (1992), 129-131. MR 93g:46076
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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:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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