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The cotype and uniform convexity of unitary ideals

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Abstract

Information about geometric properties, such as uniform convexity and smoothness, type and cotype, of a unitary Banach idealS E is obtained from properties of the symmetric Banach sequence spaceE. In particularS E has cotype 2 ifE does. The proofs use real interpolation and complex geometry.

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References

  1. J. Arazy,Some remarks on interpolation theorems and the boundness of the triangular projection in unitary matrix spaces, Integral Equations and Operator Theory1 (1978), 453–495.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Arazy,On the geometry of the unit ball of unitary matrix spaces, Integral Equations and Operator Theory4 (1981), 150–171.

    Article  MathSciNet  Google Scholar 

  3. J. Bergh and J. Löfström,Interpolation Spaces, Springer Verlag, 1976.

  4. W. J. Davis, D. J. H. Garling and N. Tomczak-Jaegermann,The complex convexity of quasinormed linear spaces, to appear.

  5. D. J. H. Garling,On ideals of operators in Hilbert space, Proc. London Math. Soc.17 (1967), 115–138.

    Article  MATH  MathSciNet  Google Scholar 

  6. I. C. Gohberg and M. G. Krein,Introduction to the theory of linear nonselfadjoint operators, Am. Math. Soc., Transl., Vol. 18.

  7. T. Holmsted,Interpolation of quasi-normed spaces, Math. Scand.26 (1970), 177–199.

    MathSciNet  Google Scholar 

  8. J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces, Vol. II, Springer Verlag, Berlin-Heidelberg-New York, 1979.

    MATH  Google Scholar 

  9. C. A. McCarthy,c p Isr. J. Math.5 (1967), 249–271.

    MathSciNet  Google Scholar 

  10. G. Pisier,Some applications of the complex interpolation method to Banach lattices, J. Analyse Math.35 (1979), 264–281.

    Article  MATH  MathSciNet  Google Scholar 

  11. G. Pisier,Sur les espaces de Banach K -convexes, Seminaire d’Analyse Fonctionelle, Ecole Polytechnique, Expose No. XI, 1979–80.

  12. N. Tomczak-Jaegermann,The moduli of convexity and smoothness and the Rademacher averages of trace classes S p (1<p<∞), Studia Math.50 (1974), 163–182.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. St. John’s College, Cambridge, England

    D. J. H. Garling & N. Tomczak-Jaegermann

  2. Department of Mathematics, Texas A & M University, 77843, College Station, TX, USA

    D. J. H. Garling & N. Tomczak-Jaegermann

  3. Institute of Mathematics, Warsaw University, Warsaw, Poland

    D. J. H. Garling & N. Tomczak-Jaegermann

Authors
  1. D. J. H. Garling
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  2. N. Tomczak-Jaegermann
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Partially supported by NSF Grant MCS-8201044

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Garling, D.J.H., Tomczak-Jaegermann, N. The cotype and uniform convexity of unitary ideals. Israel J. Math. 45, 175–197 (1983). https://doi.org/10.1007/BF02774015

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  • DOI: https://doi.org/10.1007/BF02774015

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