On the principle of local reflexivity

Ehrhard Behrends

Studia Mathematica (1991)

  • Volume: 100, Issue: 2, page 109-128
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Behrends, Ehrhard. "On the principle of local reflexivity." Studia Mathematica 100.2 (1991): 109-128. <http://eudml.org/doc/215877>.

@article{Behrends1991,
abstract = {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.},
author = {Behrends, Ehrhard},
journal = {Studia Mathematica},
keywords = {matrix-closed families of subspaces; local reflexivity theorem},
language = {eng},
number = {2},
pages = {109-128},
title = {On the principle of local reflexivity},
url = {http://eudml.org/doc/215877},
volume = {100},
year = {1991},
}

TY - JOUR
AU - Behrends, Ehrhard
TI - On the principle of local reflexivity
JO - Studia Mathematica
PY - 1991
VL - 100
IS - 2
SP - 109
EP - 128
AB - 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.
LA - eng
KW - matrix-closed families of subspaces; local reflexivity theorem
UR - http://eudml.org/doc/215877
ER -

References

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  1. [1] E. Behrends, M-Structure and the Banach-Stone Theorem, Lecture Notes in Math. 736, Springer, 1979. 
  2. [2] E. Behrends, A generalization of the principle of local reflexivity, Rev. Roumaine Math. Pures Appl. 31 (1986), 293-296. Zbl0609.46006
  3. [3] E. Behrends, A simple proof of the principle of local reflexivity, preprint, 1989. 
  4. [4] S. F. Bellenot, Local reflexivity of normed spaces, J. Funct. Anal. 59 (1984), 1-11. Zbl0551.46008
  5. [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. [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. [7] P. Domański, Operator form of the principle of local reflexivity, preprint, 1988. 
  8. [8] P. Domański, Principle of local reflexivity for operators and quojections, Arch. Math. (Basel) 54 (1990), 567-575. Zbl0673.46002
  9. [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. [10] H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart 1981. 
  11. [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. Zbl0217.16103
  12. [12] K.-D. Kürsten, Lokale Reflexivität und lokale Dualität von Ultraprodukten für halbgeordnete Banachräume, Z. Anal. Anwendungen 3 (1984), 254-262. 
  13. [13] J. Lindenstrauss and H. P. Rosenthal, The ℒ p -spaces, Israel J. Math. 7 (1969), 325-349. Zbl0205.12602
  14. [14] Ch. Stegall, A proof of the principle of local reflexivity, Proc. Amer. Math. Soc. 78 (1980), 154-156. 

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