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We use the method of interlacing families of polynomials introduced to prove two theorems known to imply a positive solution to the Kadison--Singer problem.
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R. V. Kadison and I. M. Singer · 1959
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Extensions, restrictions, and representations of states on C ∗ C^{*} -algebras
J. Anderson · 1979
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J. Anderson · 1979
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Zeros of convex combinations of polynomials
H. J. Fell · 1980
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A conjecture concerning the pure states of ℬ ( ℋ ) \mathcal{B}(\mathcal{H}) and related theorem
J. Anderson · 1981
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Geometry of polynomials
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Matrix norm inequalities and the relative dixmier property
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Mixed discriminants of positive semidefinite matrices
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Restricted invertibility of matrices and applications
J. Bourgain and L. Tzafriri · 1989
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Lyapunov theorems for operator algebras
C. A. Akemann and J. Anderson · 1991
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On a problem of Kadison and Singer
J. Bourgain and L. Tzafriri · 1991
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Obreschkoff’s theorem revisited: what convex sets are contained in the set of hyperbolic polynomials?
J. P. Dedieu · 1992
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R. B. Bapat and T. E. S. Raghavan · 1997
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M. Rudelson · 1999
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R. Ahlswede and A. Winter · 2002
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Q. I. Rahman and G. Schmeisser · 2002
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N. Weaver · 2004
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J. Borcea and P. Brändén · 2009
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The Lee-Yang and Pólya-Schur programs. II. theory of stable polynomials and applications
J. Borcea and P. Brändén · 2009
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Multivariate Polya-Schur classification problems in the Weyl algebra
J. Borcea and P. Brändén · 2010
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Minimal sequences and the Kadison–Singer problem
W. Lawton · 2010
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The Feichtinger conjecture for reproducing kernels in model subspaces
A. Baranov and K. Dyakonov · 2011
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The Kadison–Singer problem in mathematics and engineering: a detailed account
P. G. Casazza, M. Fickus, J. C. Tremain, and E. Weber · 2006
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The van der Waerden conjecture for mixed discriminants
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P. G. Casazza, D. Edidin, D. Kalra, and V. I. Paulsen · 2007
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Multivariate stable polynomials: theory and applications
D. G. Wagner · 2011
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C. A. Akemann, J. Anderson, and B. Tanbay · 2012
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Twice-Ramanujan sparsifiers
J. Batson, D. A. Spielman, and N. Srivastava · 2012
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Hyperbolicity and stable polynomials in combinatorics and probability
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Interlacing families I: Bipartite Ramanujan graphs of all degrees
A. Marcus, D. A. Spielman, and N. Srivastava · 2013
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Real stable polynomials and the Kadison-Singer problem, 2013
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