Mots-clés : relative projection constant
@article{VTPMK_2022_3_a5,
author = {O. M. Martynov},
title = {Projection constants of the space $l_\infty^{3m}$},
journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
pages = {76--90},
year = {2022},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTPMK_2022_3_a5/}
}
O. M. Martynov. Projection constants of the space $l_\infty^{3m}$. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2022), pp. 76-90. http://geodesic.mathdoc.fr/item/VTPMK_2022_3_a5/
[1] Blätter J., Cheney E. W., “Minimal projections on hyperplanes in sequence spaces”, Annali di Matematica Pura ed Applicata, 101 (1974), 215–227
[2] Kroó A., Pinkus A., “Strong uniqueness”, Surveys in Approximation Theory, 5 (2010), 1–91
[3] Lewicki G., Best Approximation in Spaces of Bounder Linear Operators, Dissertationes Mathematicae, Instytut Matematyczny Polskiej Akademii Nauk, Warszawa, 1994, 103 pp.
[4] Lewicki G., Micek A., “Equality of two strong unique projection constants”, Journal of Approximation Theory, 162:12 (2010), 2278–2289
[5] Lokot’ V. V., “On a class of minimal projections in finite dimensional spaces”, Optimization, 29 (1994), 311–317
[6] 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
[7] Lokot V. V., Martynov O. M., Projection constants, MGGU, Murmansk, 2013, 302 pp. (in Russian)
[8] 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
[9] Martynov O. M., Nekotorye svojstva operatorov proektirovaniya v banakhovykh prostranstvakh, PhD Thesis, RGPU im. A.I. Gertsena, SPb, 2002 (in Russian)
[10] 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)
[11] Martynov O. M., “On the strong uniqueness of some projections with unit norm”, Differential equations and control processes, 2 (2020), 33–48 (in Russian)
[12] Martynov O. M., “On the strong uniqueness of minimal projections in the space $l_\infty^9$”, Herald of Tver State University. Series: Applied Mathematics, 2020, no. 4, 28–42 (in Russian) | DOI
[13] Martynov O. M., “On the relative projection constants of some classes of subspaces of the space $l_\infty^{2n}$”, Functional analysis and its applications, 54:4 (2020), 98–101 (in Russian)
[14] Martynov O. M., “Constants of strong uniqueness of minimal projections onto some n-dimensional subspaces of $l_\infty^{2n} (n\geqslant 2)$”, Journal of Approximation Theory, 262 (2021), 105507
[15] Martynov O. M., “Some projections and their properties in the space $l_\infty^4$”, Some actual problems of modern mathematics and mathematical education. Herzen readings, v. LXXIV, Publishing House of A.I. Herzen RSPU, SPb., 2021, 126–132 (in Russian)
[16] Martynov O. M., “Some projections and their properties in the space $l_\infty^{mn} (m\geqslant 2, n\geqslant 3)$”, Annales Polonici Mathematici, 128:3 (2022), 221–231
[17] Odinets V. P., Minimal projectors in Banach spaces. Problems of uniqueness and existence and their applications, WSP, Bydgoszcz, 1985 (in Russian)
[18] 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)
[19] Odyniec W., Lewicki G., Minimal Projections in Banach Spaces, v. 1449, Lecture Notes in Mathematics, Springer, Berlin, New York, 1990
[20] Odyniec W., Prophet M., “The strong unicity constant and its applications”, Banach Center Publications, 79:1 (2008), 167–172 | DOI
[21] 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
[22] Odinets V. P., Yakubson M. Ya., Projectors and bases in normed spaces, Editorial URSS Publ., Moscow, 2004 (in Russian)