Mots-clés : relative projection constant
@article{VTPMK_2020_4_a2,
author = {O. M. Martynov},
title = {On the strong uniqueness of minimal projections in the space $l_\infty^9$},
journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
pages = {28--42},
year = {2020},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTPMK_2020_4_a2/}
}
TY - JOUR AU - O. M. Martynov TI - On the strong uniqueness of minimal projections in the space $l_\infty^9$ JO - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika PY - 2020 SP - 28 EP - 42 IS - 4 UR - http://geodesic.mathdoc.fr/item/VTPMK_2020_4_a2/ LA - ru ID - VTPMK_2020_4_a2 ER -
O. M. Martynov. On the strong uniqueness of minimal projections in the space $l_\infty^9$. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2020), pp. 28-42. http://geodesic.mathdoc.fr/item/VTPMK_2020_4_a2/
[1] Blätter J., Cheney E. W., “Minimal projections on hyperplanes in sequence spaces”, Annali di Matematica Pura ed Applicata, 101 (1974), 215–227 | DOI | MR | Zbl
[2] Bohnenblust H. F., “Convex regions and projections in Minkowski spaces”, Annals of Mathematics, 1938, 301–308 | DOI | MR
[3] Chalmers B.L., Lewicki G., “Three-dimensional subspace of with maximal projection constants”, Journal of Functional Analysis, 257 (2009), 553–592 | DOI | MR | Zbl
[4] König H. P., Lewis D. R., Lin P. -K., “Finite dimensional projections”, Studia Mathematica, 75:3 (1983), 341–358 | DOI | MR
[5] Lewicki G., Best Approximation in Spaces of Bounder Linear Operators, Dissertationes Mathematicae, Instytut Matematyczny Polskiej Akademii Nauk, Warszawa, 1994, 103 pp.
[6] Lewicki G., Micek A., “Equality of two strong unique projection constants”, Journal of Approximation Theory, 162:12 (2010), 2278–2289 | DOI | MR | Zbl
[7] Lokot’ V. V., “On a class of minimal projections in finite dimensional spaces”, Optimization, 29 (1994), 311–317 | DOI | MR | Zbl
[8] Lokot' V. V., “Constants of Strong Uniqueness of Minimal Projections onto Hyperplanes in the Space $l_\infty^{n} (n\geqslant 3)$”, Mathematical Notes, 72:5 (2002), 667–671 | DOI | DOI | MR | Zbl
[9] Lokot V. V., Martynov O. M., Projection constants, MGGU, Murmansk, 2013, 302 pp. (in Russian)
[10] Martinov O. M., “Constants of strong unicity of minimal projections onto some two-dimensional subspaces of $l_\infty^{4}$”, Journal of Approximation Theory, 118 (2002), 175–187 | DOI | MR | Zbl
[11] Martynov O. M., Nekotorye svojstva operatorov proektirovaniya v banakhovykh prostranstvakh, PhD Thesis, RGPU im. A.I. Gertsena, SPb, 2002 (in Russian)
[12] Martynov O. M., “Projection constants of a certain class of subspaces of codimension two in the space $l_\infty^{2n}$”, Functional analysis and its applications, 53:3 (2019), 33–44 (in Russian) | MR | Zbl
[13] Martynov O. M., “On the strong uniqueness of some projections with unit norm”, Differential equations and control processes, 2 (2020), 33–48 (in Russian) | Zbl
[14] Newman D. J., Shapiro H. S., “Some theorems on Chebyshev approximation”, Duke Mathematical Journal, 30:4 (1963), 673–681 | DOI | MR | Zbl
[15] Newman D. J., Shapiro H. S., “Approximation by Generalized Rational Functions”, On Approximation Theory, v. 5, eds. P.L. Butzer, J. Korevaar, Springer, Basel, 1964, 245–251 | DOI | MR
[16] Odinets V. P., “On the seminar on the geometry of Banach spaces in 1990-97.”, Some actual problems of modern mathematics and mathematical education. Herzen Readings 2007, v. LX, Izd-vo BAN, SPb, 2007, 12–26 (in Russian) | MR
[17] Odyniec W., Lewicki G., Minimal Projections in Banach Spaces, v. 1449, Lecture Notes in Mathematics, Springer, Berlin, New York, 1990 | DOI | MR | Zbl
[18] Odyniec W., Prophet M., “The strong unicity constant and its applications”, Banach Center Publications, 79:1 (2008), 167–172 | DOI | MR | Zbl
[19] Odyniec W., Prophet M. P., “A lower bound of the strongly unique minimal projection constant of $l_\infty^{n}, (n\geqslant 3)$”, Journal of Approximation Theory, 145 (2007), 111–121 | DOI | MR | Zbl
[20] Odinets V. P., Yakubson M. Ya., Projectors and bases in normed spaces, Editorial URSS Publ., Moscow, 2004 (in Russian)