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.
Citation:
F. A. Sukochev, S. V. Ferleger, “Harmonic analysis in (UMD)-spaces: Applications to the theory of bases”, Mat. Zametki, 58:6 (1995), 890–905; Math. Notes, 58:6 (1995), 1315–1326