Banach spaces all of whose subspaces have the approximation property

W. B. Johnson

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz") (1979-1980)

  • page 1-11

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Johnson, W. B.. "Banach spaces all of whose subspaces have the approximation property." Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz") (1979-1980): 1-11. <http://eudml.org/doc/109224>.

@article{Johnson1979-1980,
author = {Johnson, W. B.},
journal = {Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")},
keywords = {approximation property; Schauder basis; unconditional basis; not isomorphic to Hilbert space; type and cotype of a Banach space; uniform projection a.p},
language = {eng},
pages = {1-11},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Banach spaces all of whose subspaces have the approximation property},
url = {http://eudml.org/doc/109224},
year = {1979-1980},
}

TY - JOUR
AU - Johnson, W. B.
TI - Banach spaces all of whose subspaces have the approximation property
JO - Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
PY - 1979-1980
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 11
LA - eng
KW - approximation property; Schauder basis; unconditional basis; not isomorphic to Hilbert space; type and cotype of a Banach space; uniform projection a.p
UR - http://eudml.org/doc/109224
ER -

References

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  1. 1 T. Figiel and W.E. Johnson, A uniformly convex Banach space which contains no lp, Compositio Math.29 (1974), 179-190. Zbl0301.46013MR355537
  2. 2 T. Figiel and W.B. Johnson, Large subspaces of ln∞ and estimates of the Gordon-Lewis constant, Israel J. Math. (submitted) Zbl0445.46012
  3. 3 T. Figiel, S. Kwapien, and A. Pelczynski, Sharp estimates for the constants of local unconditional structure of Minkowski spaces, Bull. Acad. Polon. Sci.25(1977), 1221-1226. Zbl0379.46012MR487397
  4. 4 T. Figiel, J. Lindenstrauss, and V. Milman, The dimension of almost spherical sections of convex bodies, Acta Math.139(1977), 53-94. Zbl0375.52002MR445274
  5. 5 Y. Gordon and D.R. Lewis, Absolutely summing operators and local unconditional structures, Acta Math.133(1974), 27-48. Zbl0291.47017MR410341
  6. 6 S. Heinrich, Finite representability and super ideals of operators, Dissertationes Math. ( to appear). Zbl0443.47042MR575755
  7. 7 S. Heinrich, Ultraproducts in Banach space theory, Arkiv für Reine und Angew. Math. ( to appear). Zbl0412.46017MR552464
  8. 8 W.B. Johnson, A reflexive Banach space which is not sufficiently Euclidean, Studia Math.55(1976), 201-205. Zbl0362.46015MR430756
  9. 9 W.B. Johnson, H.P. Rosenthal, and M. Zippin, On bases, finite dimensional decompositions, and weaker structures in Banach spaces, Israel J. Math.9 (1971), 488-506. Zbl0217.16103MR280983
  10. 10 W.B. Johnson and M. Zippin, On subspaces of quotients of (ΣG n)lp and (ΣGn)co, Israel J. Math.13 (1972), 311-316. Zbl0252.46025
  11. 11 S. Kwapien, Isomorphic characterization of inner product spaces by orthogonal series with vector valued coefficients, Studia Math.44(1972), 583-595. Zbl0256.46024MR341039
  12. 12 J. Lindenstrauss and H.P. Rosenthal, the Lp spaces. Israel J. Math.7 (1969), 325-349. Zbl0205.12602MR270119
  13. 13 J. Lindenstrauss and L. Tzafiri, On the complemented subspaces problem, Israel J. Math.9 (1971), 263-269. Zbl0211.16301MR276734
  14. 14 J 'Lindenstrauss and L. Tzafriri, The uniform approximation property in Orlicz spaces, Israel J. Math.23(1976), 142-155. Zbl0347.46025MR399806
  15. 15 J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I, Sequence spaces, Ergebnisse92; Springer-Verlag (1977). Zbl0362.46013MR500056
  16. 16 J. Lindenstrauss and L. Tzafriri, Classical Banach spaces II, Function spaces, Ergebnisse97; Springer-Verlag (1979). Zbl0403.46022MR540367
  17. 17 B. Maurey, Un théorème de prolongement. C.R. Acad. Sci. Paris, Sér A-B279 (1974), 329-332. Zbl0291.47001MR355539
  18. 18 A. Pelczynski and H.P. Rosenthal, Localization techniques in L p spaces, Studia Math.52(1975), 263-289. Zbl0297.46023MR361729
  19. 19 A. Szankowski, Subspaces without approximation property, Israel J. Math.30 (1978), 123-129. Zbl0384.46008MR508257

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