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Mat. Sb., 2015, Volume 206, Number 7, Pages 95–102 (Mi msb8495)  

This article is cited in 5 scientific papers (total in 5 papers)

Lunin's method for selecting large submatrices with small norm

B. S. Kashin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: 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.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant no. 14-50-00005.


DOI: https://doi.org/10.4213/sm8495

Full text: PDF file (470 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2015, 206:7, 980–987

Bibliographic databases:

Document Type: Article
UDC: 517.983
MSC: 46B20
Received: 24.02.2015

Citation: B. S. Kashin, “Lunin's method for selecting large submatrices with small norm”, Mat. Sb., 206:7 (2015), 95–102; Sb. Math., 206:7 (2015), 980–987

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. V. Limonova, “Decomposing a matrix into two submatrices with smaller $(2,1)$-norms”, Russian Math. Surveys, 71:4 (2016), 781–783  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. B. S. Kashin, “Decomposing an orthogonal matrix into two submatrices with extremally small $(2,1)$-norm”, Russian Math. Surveys, 72:5 (2017), 971–973  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. V. N. Temlyakov, “The Marcinkiewicz-type discretization theorems for the hyperbolic cross polynomials”, Jaen J. Approx., 9:1 (2017), 37–63  mathscinet  isi
    4. Temlyakov V.N., “Universal Discretization”, J. Complex., 47 (2018), 97–109  crossref  mathscinet  zmath  isi  scopus
    5. Temlyakov V.N., “The Marcinkiewicz-Type Discretization Theorems”, Constr. Approx., 48:2 (2018), 337–369  crossref  mathscinet  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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