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1993 | 107 | 2 | 137-155
Tytuł artykułu

Estimation of the position of intermediate spaces for a Banach couple

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The position of intermediate spaces for a Banach couple is estimated with the help of its fundamental function and co-function. We study the completeness of the collection of all such functions, and the methods of calculating and estimating them for different couples. Finally, these functions are used to compare the position of spaces obtained under the action of some interpolation functors.
Słowa kluczowe
Czasopismo
Rocznik
Tom
107
Numer
2
Strony
137-155
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-11-20
poprawiono
1993-04-01
Twórcy
  • Department of Mathematics, Technion, Israel Institute of Technology, Haifa 3200, Israel
Bibliografia
  • [BK1] Yu. A. Brudnyĭ and N. Ya. Kruglyak, Real interpolation functors, Dokl. Akad. Nauk SSSR 256 (1981), 14-18 (in Russian); English transl.: Soviet Math. Dokl. 23 (1981), 5-8.
  • [BK2] Yu. A. Brudnyĭ and N. Ya. Kruglyak, Interpolation Functors and Interpolation Spaces, North-Holland, 1991.
  • [BO] M. Z. Berkolaĭko and V. I. Ovchinnikov, Inequalities for entire functions of exponential type in symmetric spaces, Trudy Mat. Inst. Steklov. 161 (1983), 3-17 (in Russian); English transl.: Proc. Steklov Inst. Math. 3 (1984), 1-17.
  • [C] A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 133-190.
  • [Cw] M. Cwikel, Monotonicity properties of interpolation spaces, Ark. Mat. 14 (1976), 213-236; 19 (1981), 123-136.
  • [D] A. A. Dmitriev, On the interpolation of one-dimensional operators, Trudy Nauchn. Issl. Inst. Mat. Voronezh. Gos. Univ. 11 (1973), 31-43 (in Russian).
  • [DKO] V. I. Dmitriev, S. G. Kreĭn and V. I. Ovchinnikov, Fundamentals of interpolation theory for linear operators, in: Geometry of Linear Spaces and Operator Theory, Yaroslavl', 1977, 31-74 (in Russian).
  • [G] J. Gustavsson, A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42 (1978), 289-305.
  • [J] S. Janson, Minimal and maximal methods of interpolation, J. Funct. Anal. 44 (1981), 50-73.
  • [KPS] S. G. Kreĭn, Yu. I. Petunin and E. M. Semenov, Interpolation of Linear Operators, Nauka, Moscow, 1978 (in Russian); English transl.: Amer. Math. Soc., Providence, 1982.
  • [M] L. Maligranda, Interpolation of operators in $A_φ$-spaces, Bull. Polish Acad. Sci. Math. 33 (1985), 289-297.
  • [MM] L. Maligranda and M. Mastyło, Notes on non-interpolation spaces, J. Approx. Theory 56 (1989), 333-347.
  • [O1] V. I. Ovchinnikov, Interpolation theorems resulting from an inequality of Grothendieck, Funktsional. Anal. i Prilozhen. 10 (1976), 45-54 (in Russian); English transl.: Functional Anal. Appl. 10 (1976), 287-294.
  • [O2] V. I. Ovchinnikov, The Method of Orbits in Interpolation Theory, Math. Rep. 1, Part 2, Harwood, 1984, 349-516.
  • [P1] E. I. Pustylnik, Minimal and maximal intermediate Banach spaces, Ukrain. Mat. Zh. 29 (1977), 129-137 (in Russian); English transl.: Ukrainian Math. J. 29 (1977), 102-107.
  • [P2] E. I. Pustylnik, Dual Banach couples, Sibirsk. Mat. Zh. 20 (1979), 603-609 (in Russian); English transl.: Siberian Math. J. 20 (1979), 421-425.
  • [P3] E. I. Pustylnik, Optimal interpolation and some interpolation properties of Orlicz spaces, Dokl. Akad. Nauk SSSR 269 (1983), 292-295 (in Russian); English transl.: Soviet Math. Dokl. 27 (1983), 333-336.
  • [P4] E. I. Pustylnik, On some structural properties of collections of intermediate spaces of any Banach couple, in: Theory of Operators in Function Spaces, Voronezh, 1983, 80-89 (in Russian).
  • [P5] E. I. Pustylnik, Families of Banach spaces with a function parameter, Izv. Vyssh. Ucheb. Zaved. Mat. 1985 (8), 79-81 (in Russian).
  • [P6] E. I. Pustylnik, On subordination relations for concave functions of selfadjoint operators, Dokl. Akad. Nauk SSSR 224 (1975), 1264-1267; English transl.: Soviet Math. Dokl. 16 (1975), 1394-1398.
  • [S] G. Sparr, Interpolation of weighted $L_p$-spaces, Studia Math. 62 (1978), 229-271.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv107i2p137bwm
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