Annales Mathématiques
Blaise Pascal

[1] C. A. Akemann; V. Paulsen State extensions and the Kadison-Singer problem (2008) (http://www.math.uh.edu/~vern/ARCC-ap.pdf)

[2] Charles A. Akemann; Joel Anderson Lyapunov theorems for operator algebras, Mem. Amer. Math. Soc., Volume 94 (1991) no. 458, pp. iv+88 | DOI | MR | Zbl

[3] Joel Anderson Extensions, restrictions, and representations of states on $C^{*}$-algebras, Trans. Amer. Math. Soc., Volume 249 (1979) no. 2, pp. 303-329 | DOI | MR | Zbl

[4] Joel Anderson Extreme points in sets of positive linear maps on $ℬ\left(\mathscr{H}\right)$, J. Funct. Anal., Volume 31 (1979) no. 2, pp. 195-217 | DOI | MR | Zbl

[5] William Arveson An invitation to $C^{*}$-algebras, Springer-Verlag, New York-Heidelberg, 1976, pp. x+106 (Graduate Texts in Mathematics, No. 39) | MR | Zbl

[6] Radu Balan; Peter G. Casazza; Christopher Heil; Zeph Landau Density, overcompleteness, and localization of frames. I. Theory, J. Fourier Anal. Appl., Volume 12 (2006) no. 2, pp. 105-143 | DOI | MR | Zbl

[7] Anton Baranov; Konstantin Dyakonov The Feichtinger conjecture for reproducing kernels in model subspaces, J. Geom. Anal., Volume 21 (2011) no. 2, pp. 276-287 | DOI | MR | Zbl

[8] Kenneth Berman; Herbert Halpern; Victor Kaftal; Gary Weiss Matrix norm inequalities and the relative Dixmier property, Integral Equations Operator Theory, Volume 11 (1988) no. 1, pp. 28-48 | DOI | MR | Zbl

[9] Tristan Matthew Bice Filters in ${\mathrm{C}}^{*}$-algebras, Canad. J. Math., Volume 65 (2013) no. 3, pp. 485-509 | DOI | MR | Zbl

[10] Bjarte Bøe An interpolation theorem for Hilbert spaces with Nevanlinna-Pick kernel, Proc. Amer. Math. Soc., Volume 133 (2005) no. 7, p. 2077-2081 (electronic) | DOI | MR | Zbl

[11] Nicolas Bourbaki Espaces vectoriels topologiques. Chapitres 1 à 5, Masson, Paris, 1981, pp. vii+368 (Éléments de mathématique. [Elements of mathematics]) | MR

[12] J. Bourgain; L. Tzafriri Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis, Israel J. Math., Volume 57 (1987) no. 2, pp. 137-224 | DOI | MR | Zbl

[13] J. Bourgain; L. Tzafriri On a problem of Kadison and Singer, J. Reine Angew. Math., Volume 420 (1991), pp. 1-43 | MR | Zbl

[14] Marcin Bownik; Darrin Speegle The Feichtinger conjecture for wavelet frames, Gabor frames and frames of translates, Canad. J. Math., Volume 58 (2006) no. 6, pp. 1121-1143 | DOI | MR | Zbl

[15] Peter G. Casazza; Ole Christensen; Nigel J. Kalton Frames of translates, Collect. Math., Volume 52 (2001) no. 1, pp. 35-54 | MR | Zbl

[16] Peter G. Casazza; Ole Christensen; Alexander M. Lindner; Roman Vershynin Frames and the Feichtinger conjecture, Proc. Amer. Math. Soc., Volume 133 (2005) no. 4, p. 1025-1033 (electronic) | DOI | MR | Zbl

[17] Peter G. Casazza; Matthew Fickus; Janet C. Tremain; Eric Weber The Kadison-Singer problem in mathematics and engineering : a detailed account, Operator theory, operator algebras, and applications (Contemp. Math.), Volume 414, Amer. Math. Soc., Providence, RI, 2006, pp. 299-355 | DOI | MR | Zbl

[18] Peter G. Casazza; Jesse Peterson An elementary, illustrative proof of the Rado-Horn theorem, Linear Algebra Appl., Volume 437 (2012) no. 10, pp. 2523-2537 | DOI | MR | Zbl

[19] I. Chalendar; E. Fricain; D. Timotin A short note on the Feichtinger conjecture (2011) (http://arxiv.org/abs/1106.3408) | MR

[20] Gustave Choquet Deux classes remarquables d’ultrafiltres sur N, Bull. Sci. Math. (2), Volume 92 (1968), pp. 143-153 | MR | Zbl

[21] P. A. M. Dirac The Principles of Quantum Mechanics, Oxford, at the Clarendon Press, 1930

[22] Jacques Dixmier Les $C^{*}$-algèbres et leurs représentations, Deuxième édition. Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars Éditeur, Paris, 1969, pp. xv+390 | Zbl

[23] Ronald G. Douglas Banach algebra techniques in operator theory, Graduate Texts in Mathematics, 179, Springer-Verlag, New York, 1998, pp. xvi+194 | DOI | MR | Zbl

[24] R. J. Duffin; A. C. Schaeffer A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., Volume 72 (1952), pp. 341-366 | MR | Zbl

[25] Fricain E.; J. Mashreghi Theory of de Branges-Rovnyak spaces (Cambridge University Press, à paraître)

[26] Pasc Găvruţa On the Feichtinger conjecture, Electron. J. Linear Algebra, Volume 26 (2013), pp. 546-552 | DOI | MR | Zbl

[27] Kevin Gregson Extensions of pure states of $C^{*}$-$$algebras, University of Aberdeen (UK) (1986) (Ph. D. Thesis)

[28] Karlheinz Gröchenig Localized frames are finite unions of Riesz sequences, Adv. Comput. Math., Volume 18 (2003) no. 2-4, pp. 149-157 (Frames) | DOI | MR | Zbl

[29] Herbert Halpern; Victor Kaftal; Gary Weiss The relative Dixmier property in discrete crossed products, J. Funct. Anal., Volume 69 (1986) no. 1, pp. 121-140 | DOI | MR | Zbl

[30] N. J. A. Harvey An introduction to the Kadison-Singer problem and the paving conjecture (2013) (www.cs.ubc.ca/~nickhar/Publications/KS/KS.pdf)

[31] P. Jaming Inversibilité restreinte, problème d’extension de Kadison-Singer et applications à l’analyse harmonique (d’après J. Bourgain et L. Tzafriri), Cours : analyse fonctionnelle et harmonique (1992–1993) (Publ. Math. Orsay), Volume 94, Univ. Paris XI, Orsay, 1994, pp. 71-154 (http://www.univ-orleans.fr/mapmo/membres/jaming/articles/memoire/memoire.html) | Zbl

[32] Richard V. Kadison; I. M. Singer Extensions of pure states, Amer. J. Math., Volume 81 (1959), pp. 383-400 | MR | Zbl

[33] Alexander S. Kechris Classical descriptive set theory, Graduate Texts in Mathematics, 156, Springer-Verlag, New York, 1995, pp. xviii+402 | DOI | MR | Zbl

[34] Sneh Lata; Vern Paulsen The Feichtinger conjecture and reproducing kernel Hilbert spaces, Indiana Univ. Math. J., Volume 60 (2011) no. 4, pp. 1303-1317 | DOI | MR | Zbl

[35] Adam Marcus; Daniel A. Spielman; Nikhil Srivastava Interlacing families I : bipartite Ramanujan graphs of all degrees (2013) (http://arxiv.org/abs/1304.4132) | MR

[36] Adam Marcus; Daniel A. Spielman; Nikhil Srivastava Interlacing families II : mixed characteristic polynomials and the Kadison-Singer problem (2013) (http://arxiv.org/abs/1306.3969) | MR

[37] Adam Marcus; Daniel A. Spielman; Nikhil Srivastava Ramanujan graphs and the solution to the Kadison-Singer problem (2014) (http://arxiv.org/abs/1408.4421)

[38] P. J. McKenna Discrete Carleson measures and some interpolation problems, Michigan Math. J., Volume 24 (1977) no. 3, pp. 311-319 | MR | Zbl

[39] N. K. Nikolʼskiĭ Treatise on the shift operator, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 273, Springer-Verlag, Berlin, 1986, pp. xii+491 (Spectral function theory, With an appendix by S. V. Hruščev and V. V. Peller, Translated from the Russian by Jaak Peetre) | DOI | MR

[40] Vern I. Paulsen A dynamical systems approach to the Kadison-Singer problem, J. Funct. Anal., Volume 255 (2008) no. 1, pp. 120-132 | DOI | MR | Zbl

[41] Sorin Popa A ${\mathrm{II}}_1$ factor approach to the Kadison-Singer problem, Comm. Math. Phys., Volume 332 (2014) no. 1, pp. 379-414 | DOI | MR

[42] G. A. Reid On the Calkin representations, Proc. London Math. Soc. (3), Volume 23 (1971), pp. 547-564 | MR | Zbl

[43] Kristian Seip Interpolation and sampling in spaces of analytic functions, University Lecture Series, 33, American Mathematical Society, Providence, RI, 2004, pp. xii+139 | DOI | MR | Zbl

[44] D. Serre Les matrices : théorie et pratique., Dunod, 2001, pp. vii + 168 | MR | Zbl

[45] H. S. Shapiro; A. L. Shields On some interpolation problems for analytic functions, Amer. J. Math., Volume 83 (1961), pp. 513-532 | MR | Zbl

[46] Daniel A. Spielman; Nikhil Srivastava An elementary proof of the restricted invertibility theorem, Israel J. Math., Volume 190 (2012), pp. 83-91 | DOI | MR | Zbl

[47] Betül Tanbay Pure state extensions and compressibility of the $l_1$-algebra, Proc. Amer. Math. Soc., Volume 113 (1991) no. 3, pp. 707-713 | DOI | MR | Zbl

[48] Terry Tao Real stable polynomials and the Kadison-Singer problem (2013) (https://terrytao.wordpress.com/2013/11/04/real-stable-polynomials-and-the-kadison-singer-problem/)

[49] Dan Timotin The solution to the Kadison-Singer Problem - yet another presentation (2015) (http://arxiv.org/abs/1501.00464)

[50] Joel A. Tropp The random paving property for uniformly bounded matrices, Studia Math., Volume 185 (2008) no. 1, pp. 67-82 | DOI | MR | Zbl

[51] Alain Valette Le problème de Kadison-Singer (d’après A. Marcus, D. Spielman et N. Srivastava), Astérisque (2015) no. 367-368, pp. 451-476 | MR

[52] Nik Weaver A counterexample to a conjecture of Akemann and Anderson, Bull. London Math. Soc., Volume 35 (2003) no. 1, pp. 65-71 | DOI | MR | Zbl

[53] Nik Weaver The Kadison-Singer problem in discrepancy theory, Discrete Math., Volume 278 (2004) no. 1-3, pp. 227-239 | DOI | MR | Zbl

[54] Pierre Youssef Restricted invertibility and the Banach-Mazur distance to the cube, Mathematika, Volume 60 (2014) no. 1, pp. 201-218 | DOI | MR | Zbl