Dimensional gradations and cogradations of operator ideals. The weak distance between Banach-spaces

N. Tomczak-Jaegermann

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz") (1980-1981)

  • page 1-30

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Tomczak-Jaegermann, N.. "Dimensional gradations and cogradations of operator ideals. The weak distance between Banach-spaces." Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz") (1980-1981): 1-30. <http://eudml.org/doc/109259>.

@article{Tomczak1980-1981,
author = {Tomczak-Jaegermann, N.},
journal = {Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")},
keywords = {gradations of a Banach ideal of operators; (q,r)-summing norms; Gaussian type p and cotype q ideal norms; local Maurey-type extension theorem; p- factorable operators; submultiplicativity; cogradation; (t,s)-nuclear norm; normification; weak Banach-Mazur distance},
language = {eng},
pages = {1-30},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Dimensional gradations and cogradations of operator ideals. The weak distance between Banach-spaces},
url = {http://eudml.org/doc/109259},
year = {1980-1981},
}

TY - JOUR
AU - Tomczak-Jaegermann, N.
TI - Dimensional gradations and cogradations of operator ideals. The weak distance between Banach-spaces
JO - Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
PY - 1980-1981
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 30
LA - eng
KW - gradations of a Banach ideal of operators; (q,r)-summing norms; Gaussian type p and cotype q ideal norms; local Maurey-type extension theorem; p- factorable operators; submultiplicativity; cogradation; (t,s)-nuclear norm; normification; weak Banach-Mazur distance
UR - http://eudml.org/doc/109259
ER -

References

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  1. [1] Bennet, G., Dor, L.E., Goodman, V., Johnson, W.B., and Newman, C.M., ''On uncomplemented subspaces of L p, 1 &lt; p &lt; 2, Israel J. Math.26 (1977), 178-187. Zbl0339.46022MR435822
  2. [2] Davis, W.J., Milman, V.D. and Tomczak-Jaegermann, N.: "The diameter of the space of n-dimensional spaces", Israel J. Math, to appear. Zbl0475.46010
  3. [3] Figiel, T., Lindenstrauss, J. and Milman, V.D.: "The dimension of almost spherical sections of convex bodies", Acta Math.139 (1977), 53-94. Zbl0375.52002MR445274
  4. [4] Figiel, T. and Tomczak-Jaegermann, N.: "Projections onto Hilbertian subspaces of Banach spaces", Israel J. Math, 33 (1979), 155-171. Zbl0427.46010MR571251
  5. [5] Gluskin, E.D.: "Diameter of Minhowski compactum is approximately equal to n", Funk. Anal. i Pril. 15 (1981), 72-73, (Russian). Zbl0469.46017MR609798
  6. [6] John, F.: "Extremum problems with inequalities as subsidiary conditions", Courant Anniversary Volume, Interscience, New-York, 1948, 187-204. Zbl0034.10503MR30135
  7. [7] König, H.: "Type constants and (q,2)-summing norms" Israel J. Math. Zbl0449.47037
  8. [8] König, H.: "Some estimates for type and cotype constants", Séminaire d'Analyse Fonct. Ecole Polytechnique, 1979-80, Exp. 28. Zbl0441.46019MR604409
  9. [9] König, H., Retherford, J.R. and Tomczak-Jaegermann, N.: "On the eigenvalues of (p,2)-summing operators and constants associated with normed spaces", J. Fun. Anal.37(1980), 88-126. Zbl0434.47033MR576647
  10. [10] König, H. and Trafriri, L.: "Some estimates for type and cotype constants". Zbl0459.46011
  11. [11] Kwapien S.: "On operators factorizable through Lp-spaces", Bull. Soc. Math. France, Mém.31-32(1972), 215-225. Zbl0246.47040MR397464
  12. [12] Lewis, D.R.: "Ellipsoids defined by Banach ideal norms", Mathematika26(1979), 18-29. Zbl0438.46006MR557122
  13. [13] Maurey, B.: "Un théorème de prolongement", C.R. Acad. Sci. Paris279(1974), 329-332. Zbl0291.47001MR355539
  14. [14] Maurey, B. and Pisier, G.: "Séries des variables aléatoires vectoreilles indépendants et propriétés géométriques des espaces de Banach", Studia Math.58(1976), 45-90. Zbl0344.47014MR443015
  15. [15] Pełczynski A.: "Geometry of finite dimensional Banach spaces and operator ideals", Notes in Banach spaces, Univ. of Texas Press (1980). Zbl0461.46014
  16. [16] Pietsch A.: "Operator ideals", VEB Deutscher Verlag der Wissenschaften, Berlin1978. Zbl0399.47039MR519680
  17. [17] Pisier, G.: "Estimation des distances a un espace euclidien et des constantes de projection des espaces de Banach de dimension finie ", Séminaire d'Analyse Fonct. Ecole Polytechnique, 1978-79, Exp. 10. Zbl0412.46009MR520216
  18. [18] Tomczak -Jaegermann, N.: "Computing 2-summing norm with few vectors ", Ark. Math.17(1979), 273-277. Zbl0436.47033MR608320
  19. [19] Tomczak -Jaegermann, N.: "The distance between a symmetric space and a 2-convex or 2-concave space", J. London Math. Soc. to appear. Zbl0468.46008MR631939
  20. [20] Tomczak -Jaegermann, N.: "Finite-dimensional operator ideals and the Banach-Mazur distance", in preparation. Zbl0721.46004
  21. [21] Deschaseaux, J.-P.: "Une caractérisation de certains espaces vectoriels normés de dimension finie par leur constante de Macphail" C.R. Acad. Sci. Paris276(1973) A1349-A1351. Zbl0257.46016MR318841
  22. [22] Garling, D.J.H.: "Operators with large trace and a characterization of ln"∞, Proc. Camb. Phil. Soc.76(1974), 413-414. Zbl0286.47020

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