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Continuity of operators in spaces of vector functions, with applications to the theory of bases

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Abstract

Banach spaces with unconditional martingale differences are investigated. In Sec. 1 a survey of their fundamental properties and connections with vector-valued harmonic analysis is given. In Sec. 2 new results are obtained regarding bases in the spaces E(X), where E is a symmetric space.

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  1. A. V. Bukhvalov
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 5–22, 1987.

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Bukhvalov, A.V. Continuity of operators in spaces of vector functions, with applications to the theory of bases. J Math Sci 44, 749–762 (1989). https://doi.org/10.1007/BF01463181

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