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Harmonic analysis in (UMD)-spaces: Applications to the theory of bases. (English. Russian original) Zbl 0857.46006

Math. Notes 58, No. 6, 1315-1326 (1995); translation from Mat. Zametki 58, No. 6, 890-905 (1995).
Summary: 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.

MSC:

46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
46L51 Noncommutative measure and integration
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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References:

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