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Asymmetry and projection constants of Banach spaces

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Abstract

We discuss various asymmetry constants of finite-dimensional Banach spaces in a more generalized frame than that of [2], and solve a problem raised in [7] by finding an increasing sequence of Banach spaces whose diagonal asymmetry constants tend to infinity. We investigate the question of whether the projection constant of everyn-dimensional Banach space is strictly less than\(\sqrt n \), and show that this is so whenn=2.

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References

  1. W. J. Davis,Remarks on finite rank projections, to appear.

  2. D. J. H. Garling and Y. Gordon,Relations between some constants associated with finite dimensional Banach spaces, Israel J. Math.9 (1971), 346–361.

    MATH  MathSciNet  Google Scholar 

  3. Y. Gordon,On p-absolutely summing constants of Banach spaces, Israel. J. Math.7 (1969), 151–163.

    MATH  MathSciNet  Google Scholar 

  4. Y. Gordon, D. R. Lewis and J. R. Retherford,Banach ideals of operators with applications to the finite dimensional structure of Banach spaces, Israel J. Math.13 (1973), 348–360.

    MathSciNet  Google Scholar 

  5. A. Grothendieck,Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Mat. São Paulo8 (1956), 1–79.

    Google Scholar 

  6. B. Grünbaum,Projection constants, Trans. Amer. Math. Soc.95 (1960), 451–465.

    Article  MATH  MathSciNet  Google Scholar 

  7. V. I. Gurarii, M. I. Kadec, and V. I. Macaev,On Banach-Mazur distance between certain Minkowski spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.13 (1965), 719–722.

    MathSciNet  Google Scholar 

  8. F. John,Extremum problems with inequalities as subsidiary conditions, Courant Anniversary Volume, Interscience, New York, 1948, 187–204.

    Google Scholar 

  9. M. I. Kadec, to appear in Funckional Anal. i Prilôzen.

  10. S. Kwapien,On a theorem of L. Schwartz and its applications to absolutely summing operators, Studia Math.38 (1970), 193–201.

    MATH  MathSciNet  Google Scholar 

  11. A. Persson and A. Pietsch,p-nukleare und p-integrale Abbildungen in Banachräumen, Studia Math.33 (1969), 19–62.

    MATH  MathSciNet  Google Scholar 

  12. A. Pietsch,Absolute p-summierende Abbildungen in normierten Räumen, Studia Math.28 (1967), 333–353.

    MATH  MathSciNet  Google Scholar 

  13. A. Pietsch,Adjungierte normierten Operatorenideale, Math. Nach.48 (1971), 189–211.

    Article  MATH  MathSciNet  Google Scholar 

  14. H. P. Rosenthal,On subspaces of L p, to appear.

  15. D. Rutovitz,Some parameters associated with finite-dimensional Banach spaces. J. London Math. Soc.40 (1965), 241–255.

    Article  MATH  MathSciNet  Google Scholar 

  16. P. Saphar,Produits tensoriels d’espaces des Banach et classes d’applications linéaires, Studia Math.38 (1970), 71–100.

    MATH  MathSciNet  Google Scholar 

  17. R. Schatten,A theory of cross-spaces, Princeton, 1950.

  18. Y. Gordon and D. R. Lewis,Absolutely summing, L 1 factorizable operators and applications, to appear.

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The research for this paper was partially supported by NSF-GP-34193.

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Gordon, Y. Asymmetry and projection constants of Banach spaces. Israel J. Math. 14, 50–62 (1973). https://doi.org/10.1007/BF02761534

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  • DOI: https://doi.org/10.1007/BF02761534

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