Geodesic
Harmonic analysis in (UMD)-spaces: Applications to the theory of bases
Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 890-905.

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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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F. A. Sukochev; S. V. Ferleger. Harmonic analysis in (UMD)-spaces: Applications to the theory of bases. Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 890-905. http://geodesic.mathdoc.fr/item/MZM_1995_58_6_a8/

[1] Bukhvalov A. V., “Nepreryvnost operatorov v prostranstvakh vektor-funktsii: prilozheniya k teorii bazisov”, Zapiski nauch. sem. LOMI, 157, Nauka, L., 1987, 5–22 | Zbl

[2] Berkson E., Gillespie T. A., Muhly P. S., “Generalized analiticity in {UMD} spaces”, Arkiv for Math., 27 (1989), 1–14 | DOI | MR | Zbl

[3] Edvards R., Ryady Fure v sovremennom izlozhenii, T. 2, Mir, M., 1985

[4] Kashin B. S., Saakyan A. A., Ortogonalnye ryady, Nauka, M., 1984 | Zbl

[5] Lindenstrauss J., Tzafriri L., Classical Banach spaces, V. I, Springer-Verlag, New York, 1977

[6] Ellis H. W., “On the basis problem for vector-valued functional spaces”, Canad. J. Math., 1956, no. 8, 412–422 | MR

[7] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978

[8] Lindenstrauss J., Tzafriri L., Classical Banach spaces, V. II, Springer-Verlag, New York, 1979 | Zbl

[9] Morgentaller G. W., “On Walsh–Fourier series”, Trans. Amer. Math. Soc., 84:2 (1957), 472–507 | DOI | MR

[10] Berkson E., Gillespie T. A., Muhly P. S., “Theorie spectrale dans les espaces {UMD}”, C. R. Acad. Sci. Paris, 302 (1986), 155–158 | MR | Zbl

[11] Sukochev F. A., Chilin V. I., “Simmetrichnye prostranstva na polukonechnykh algebrakh fon Neimana”, DAN SSSR, 313:4 (1990), 811–815 | MR

[12] Sakai S., $C^*$-algebras and $W^*$-algebras, Springer-Verlag, New York, 1971 | Zbl