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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A Banach couple is determined by the collection of its interpolation spaces
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by O. E. Tikhonov and L. V. Veselova PDF
Proc. Amer. Math. Soc. 126 (1998), 1049-1054 Request permission

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
  • N. Aronszajn and E. Gagliardo, Interpolation spaces and interpolation methods, Ann. Mat. Pura Appl. (4) 68 (1965), 51–117. MR 226361, DOI 10.1007/BF02411022
  • Yu. A. Brudnyĭ and N. Ya. Krugljak, Interpolation functors and interpolation spaces. Vol. I, North-Holland Mathematical Library, vol. 47, North-Holland Publishing Co., Amsterdam, 1991. Translated from the Russian by Natalie Wadhwa; With a preface by Jaak Peetre. MR 1107298
  • Yu. A. Brudnyĭ, S. G. Kreĭn, and E. M. Semënov, Interpolation of linear operators, Mathematical analysis, Vol. 24 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1986, pp. 3–163, 272 (Russian). Translated in J. Soviet Math 42 (1988), no. 6, 2009–2112. MR 887950
  • S. G. Kreĭn, Yu. Ī. Petunīn, and E. M. Semënov, Interpolation of linear operators, Translations of Mathematical Monographs, vol. 54, American Mathematical Society, Providence, R.I., 1982. Translated from the Russian by J. Szűcs. MR 649411
  • 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).
  • 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).
  • L. V. Veselova and O. E. Tikhonov, On the uniqueness of the solution of an inverse problem of normal interpolation, Funktsional. Anal. i Prilozhen. 26 (1992), no. 2, 67–68 (Russian); English transl., Funct. Anal. Appl. 26 (1992), no. 2, 129–131. MR 1173087, DOI 10.1007/BF01075277
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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
  • 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 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 1049-1054
  • MSC (1991): Primary 46B70; Secondary 46M35
  • DOI: https://doi.org/10.1090/S0002-9939-98-04209-9
  • MathSciNet review: 1443170