Geodesic
Norms of random matrices and widths of finite-dimensional sets
Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 173-182 
E. D. Gluskin. Norms of random matrices and widths of finite-dimensional sets. Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 173-182. http://geodesic.mathdoc.fr/item/SM_1984_48_1_a8/
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     title = {Norms of random matrices and widths of finite-dimensional sets},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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, No 13, p. 5–10). Bibliography: 12 titles.

[1] Stechkin S. B., “O nailuchshem priblizhenii zadannykh klassov funktsii lyubymi polinomami”, UMN, IX:1 (1954), 133–134

[2] Pietsch A., “$s$-numbers of operators in Banach spaces”, Studia Math., 51 (1974), 201–223 | MR | Zbl

[3] Stesin M. I., “Aleksandrovskie poperechniki konechnomernykh mnozhestv i klassov gladkikh funktsii”, DAN SSSR, 220:6 (1975), 1278–1281 | MR | Zbl

[4] Ismagilov R. S., “Poperechniki mnozhestv v lineinykh normirovannykh prostranstvakh i priblizhenie funktsii trigonometricheskimi mnogochlenami”, UMN, XXIX:3 (1974), 161–178 | MR

[5] Kashin B. S., “O poperechnikakh oktaedrov”, UMN, XXX:4 (1975), 251–252

[6] Kashin B. S., “Poperechniki nekotorykh konechnomernykh mnozhestv i klassov gladkikh funktsii”, Izv. AN SSSR. Seriya matem., 41 (1977), 334–351 | Zbl

[7] Kashin B. S., “O nekotorykh svoistvakh matrits ogranichennykh operatorov iz prostranstva $l_2^n$ v $l_2^m$”, Izv. AN ArmSSR. Matematika, XV:5 (1980), 379–394 | MR

[8] Hölig K., “Approximationzahlen von Sobolev–Einbettungen”, Math. Ann., 242:3 (1979), 273–281 | DOI | MR

[9] Gluskin E. D., “O nekotorykh konechnomernykh zadachakh teorii poperechnikov”, Vestn. LGU, 1981, no. 13, 5–10 | MR | Zbl

[10] Mityagin B. S., “Sluchainye matritsy i podprostranstva”, Geometriya lineinykh prostranstv i teoriya operatorov, Yaroslavl, 1977, 175–202 | MR | Zbl

[11] Kolmogorov A. N., Tikhomirov V. M., “$\varepsilon$-entropiya i $\varepsilon$-emkost mnozhestv v funktsionalnykh prostranstvakh”, UMN, XIV:2 (1959), 3–86 | MR

[12] Fiegel T., Lindenstrauss J., Milman V. D., “The dimension of almost spherical sections of convex bodies”, Acta math., 139 (1977), 53–94 | DOI | MR