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Invertibility threshold for $H^\infty$ trace algebras, and effective matrix inversions
Algebra i analiz, Tome 23 (2011) no. 1, pp. 87-110.

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V. I. Vasyunin; N. K. Nikolskiǐ. Invertibility threshold for $H^\infty$ trace algebras, and effective matrix inversions. Algebra i analiz, Tome 23 (2011) no. 1, pp. 87-110. http://geodesic.mathdoc.fr/item/AA_2011_23_1_a2/

[1] ARCC Workshop: The Kadison–Singer Problem http://www.aimath.org/WWN/kadisonsinger/

[2] Bourgain J., Tzafriri L., “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

[3] Casazza P. G., Christensen O., Lindner A. M., Vershynin R., “Frames and the Feichtinger conjecture”, Proc. Amer. Math. Soc., 133 (2005), 1025–1033 | DOI | MR | Zbl

[4] Casazza P. G., Tremain J. C., “The Kadison–Singer problem in mathematics and engineering”, Proc. Nat. Acad. Sci. USA, 103 (2006), 2032–2039 | DOI | MR | Zbl

[5] Garnett J. B., “Bounded analytic functions”, Pure Appl. Math., 96, Acad. Press, New York–London, 1981 | MR | Zbl

[6] Gorkin P., Mortini R., Nikolski N., “Norm controlled inversions and a corona theorem for $H^\infty$-quotient algebras”, J. Funct. Anal., 255 (2008), 854–876 | DOI | MR | Zbl

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

[8] Treatise on the shift operator, Grundlehren Math. Wiss., 273, Springer-Verlag, Berlin, 1986 | MR | MR

[9] Nikolski N., Operators, functions, and systems, v. 1, Math. Surveys Monogr., 92, Amer. Math. Soc., Providence, RI, 2002 | MR | Zbl

[10] Spielman D. A., Srivastava N., An elementary proof of the restricted invertibility theorem, February 2, 2010, arXiv: 0911.1114v3