Projection constants of the space $l_\infty^{3m}$
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2022), pp. 76-90 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper considers minimal projections of the space $l_\infty^{3m}$ on some subspace of codimension $m$. Relative projection constants are found for them, and in the case of a minimal projection with a unit norm, the maximum value of the strong uniqueness constant is found. The projection constants found can be used in computational mathematics, in particular, to assess the convergence of projection methods for solving operator equations.
Keywords: space, subspace, projection operator, the constant of strong uniqueness.
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/}
}
TY  - JOUR
AU  - O. M. Martynov
TI  - Projection constants of the space $l_\infty^{3m}$
JO  - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
PY  - 2022
SP  - 76
EP  - 90
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VTPMK_2022_3_a5/
LA  - ru
ID  - VTPMK_2022_3_a5
ER  - 
%0 Journal Article
%A O. M. Martynov
%T Projection constants of the space $l_\infty^{3m}$
%J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
%D 2022
%P 76-90
%N 3
%U http://geodesic.mathdoc.fr/item/VTPMK_2022_3_a5/
%G ru
%F 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)