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Harmonic analysis in (UMD)-spaces: Applications to the theory of bases

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Abstract

In the paper, a general method for the construction of bases and unconditional finite-dimensional basis decompositions for spaces with the property of unconditional martingale differences is proposed. The construction makes use of a certain strongly continuous representation of Cantor's group in these spaces. The results are applied to vector function spaces and symmetric spaces of measurable operators associated with factors of type II.

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Authors and Affiliations

  1. Tashkent State University, Istanbul

    F. A. Sukochev & S. V. Ferleger

Authors
  1. F. A. Sukochev
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  2. S. V. Ferleger
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Translated fromMatematicheskie Zametki, Vol. 58, No. 6, pp. 890–905, December, 1995.

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Sukochev, F.A., Ferleger, S.V. Harmonic analysis in (UMD)-spaces: Applications to the theory of bases. Math Notes 58, 1315–1326 (1995). https://doi.org/10.1007/BF02304891

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  • DOI: https://doi.org/10.1007/BF02304891

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