Geodesic
Lunin's method for selecting large submatrices with small norm
Sbornik. Mathematics, Tome 206 (2015) no. 7, pp. 980-987 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using an approach proposed by Lunin in 1989, upper bounds are found for the norms of large submatrices of a fixed $(N\times n)$-matrix which defines an operator from $l_2^n$ into $l_1^N$ with unit norm. Bibliography: 15 titles.
Keywords: submatrix, operator norm, Lunin's lemma, Kadison-Singer problem. 
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B. S. Kashin. Lunin's method for selecting large submatrices with small norm. Sbornik. Mathematics, Tome 206 (2015) no. 7, pp. 980-987. http://geodesic.mathdoc.fr/item/SM_2015_206_7_a3/

[1] B. S. Kashin, “Ob odnom svoistve bilineinykh form”, Soobsch. AN GruzSSR, 97:1 (1980), 29–32 | MR | Zbl

[2] B. S. Kashin, “On some properties of matrices of bounded operators from the space $l_2^n$ into $l_2^m$”, Soviet J. Contemporary Math. Anal., 15:5 (1980), 44–57 | MR | Zbl

[3] A. A. Lunin, “Operator norms of submatrices”, Math. Notes, 45:3 (1989), 248–252 | DOI | MR | Zbl

[4] J. Bourgain, L. Tzafriri, “Invertibility of ‘large’ submatrices with applications to the geometry of Banach spaces and harmonic analysis”, Israel J. Math., 57:2 (1987), 137–224 | DOI | MR | Zbl

[5] J. Bourgain, L. Tzafriri, “On a problem of Kadison and Singer”, J. Reine Angew. Math., 420 (1991), 1–43 | MR | Zbl

[6] R. V. Kadison, I. M. Singer, “Extensions of pure states”, Amer. J. Math., 81:2 (1959), 383–400 | DOI | MR | Zbl

[7] M. Rudelson, “Almost orthogonal submatrices of an orthogonal matrix”, Israel J. Math., 111:1 (1999), 143–155 | DOI | MR | Zbl

[8] R. Vershynin, “John's decompositions: selecting a large part”, Israel J. Math., 122:1 (2001), 253–277 | DOI | MR | Zbl

[9] J. Batson, D. A. Spielman, N. Srivastava, “Twice-Ramanujan sparsifiers”, SIAM J. Comput., 41:6 (2012), 1704–1721 | DOI | MR | Zbl

[10] B. Kashin, L. Tzafriri, Some remarks on the restrictions of operators to coordinate subspaces, Preprint No 12, Hebrew Univ. of Jerusalem, Jerusalem, 1993/94, 14 pp. www.mi.ras.ru/~kashin/download/preprint93.pdf

[11] Sh. Nitzan, A. Olevskii, A. Ulanovskii, “A few remarks on sampling of signals with small spectrum”, Proc. Steklov Inst. Math., 280 (2013), 240–247 | DOI | MR | Zbl

[12] P. Youssef, “Restricted invertibility and the Banach–Mazur distance to the cube”, Mathematica, 60:1 (2014), 201–218 | DOI | MR | Zbl

[13] A. W. Marcus, D. A. Spielman, N. Srivastava, “Interlacing families II: Mixed characteristic polynomials and the Kadison–Singer problem”, Ann. of Math. (2), 182:1 (2015), 327–350 ; arXiv: 1306.3969 | DOI

[14] N. Weaver, “The Kadison–Singer problem in discrepancy theory”, Discrete Math., 278:1-3 (2004), 227–239 | DOI | MR | Zbl

[15] B. S. Kashin, A. A. Saakyan, Orthogonal series, Transl. Math. Monogr., 75, Amer. Math. Soc., Providence, RI, 1989, xii+451 pp. | MR | MR | Zbl | Zbl