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1991 | 100 | 2 | 109-128
Tytuł artykułu

On the principle of local reflexivity

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove a version of the local reflexivity theorem which is, in a sense, the most general one: our main theorem characterizes the conditions which can be imposed additionally on the usual local reflexivity map provided that these conditions are of a certain general type. It is then shown how known and new local reflexivity theorems can be derived. In particular, the compatibility of the local reflexivity map with subspaces and operators is investigated.
Słowa kluczowe
Czasopismo
Rocznik
Tom
100
Numer
2
Strony
109-128
Opis fizyczny
Daty
wydano
1991
otrzymano
1990-08-10
poprawiono
1990-12-27
Twórcy
  • Institut für Mathematik I, Freie Universität Berlin, Arnimallee 2-6, 1000 Berlin 33, Germany
Bibliografia
  • [1] E. Behrends, M-Structure and the Banach-Stone Theorem, Lecture Notes in Math. 736, Springer, 1979.
  • [2] E. Behrends, A generalization of the principle of local reflexivity, Rev. Roumaine Math. Pures Appl. 31 (1986), 293-296.
  • [3] E. Behrends, A simple proof of the principle of local reflexivity, preprint, 1989.
  • [4] S. F. Bellenot, Local reflexivity of normed spaces, J. Funct. Anal. 59 (1984), 1-11.
  • [5] S. J. Bernau, A unified approach to the principle of local reflexivity, in: Notes in Banach Spaces, Austin 1975-79, H. E. Lacey (ed.), Univ. Texas Press, Austin, Tex., 1980, 427-439.
  • [6] D. W. Dean, The equation L(E,X**) = L(E,X)** and the principle of local reflexivity, Proc. Amer. Math. Soc. 40 (1973), 146-148.
  • [7] P. Domański, Operator form of the principle of local reflexivity, preprint, 1988.
  • [8] P. Domański, Principle of local reflexivity for operators and quojections, Arch. Math. (Basel) 54 (1990), 567-575.
  • [9] V. A. Geĭler and I. I. Chuchaev, General principle of local reflexivity and its applications to the theory of duality of cones, Sibirsk. Mat. Zh. 23 (1) (1982), 32-43 (in Russian).
  • [10] H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart 1981.
  • [11] J. B. Johnson, H. P. Rosenthal and M. Zippin, On bases, finite dimensional decompositions and weaker structures in Banach space, Israel J. Math. 9 (1971), 488-506.
  • [12] K.-D. Kürsten, Lokale Reflexivität und lokale Dualität von Ultraprodukten für halbgeordnete Banachräume, Z. Anal. Anwendungen 3 (1984), 254-262.
  • [13] J. Lindenstrauss and H. P. Rosenthal, The $ℒ_p$-spaces, Israel J. Math. 7 (1969), 325-349.
  • [14] Ch. Stegall, A proof of the principle of local reflexivity, Proc. Amer. Math. Soc. 78 (1980), 154-156.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv100i2p109bwm
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