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Norms of random matrices and widths of finite-dimensional sets

E. D. Gluskin


Abstract: Precise orders are given for the Kolmogorov and linear widths of the unit ball of the space $l_p^m$ in the metric of $l_q^m$ for $q<\infty$. The determination of the upper estimates is based on approximation by random objects. This method goes back to Kashin (Izv. Akad. Nauk SSSR, Ser. Mat., 1977, vol. 41, p. 334–351). The corresponding lower estimates were obtained in a previous article of the author (Vestn. Leningr. Univ., 1981, № 13, p. 5–10).
Bibliography: 12 titles.

UDC: 517.98

MSC: Primary 15A52, 46B20; Secondary 26A12, 41A99, 52A20

Received: 30.04.1982

 English version: Mathematics of the USSR-Sbornik, 1984, 48:1, 173–182

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