Abstract
The results mentioned in the title consist in the equivalence of the following X: 1)
, where d(·, ·) is the Banach-Mazur distance; 2) the natural projection from L2([0, 1], X) onto the subspace
,
are the Rademacher functions, k=1, 2,...} is continuous. In the paper one gives a new proof of this result, distinguished by the use of significantly less refined analytic tools than those used by Pisier.
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G. Pisier, to be published.
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This work is partially supported by NSF (MCG-8002393).
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 107, pp. 160–168, 1982.
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Figiel, T. A recent result of G. Pisier. J Math Sci 36, 398–403 (1987). https://doi.org/10.1007/BF01839611
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DOI: https://doi.org/10.1007/BF01839611