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Abstrakty
Given a finite set X ⊆ R we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the Schur–Horn theorem from a finite-dimensional setting to an infinite-dimensional Hilbert space analogous to Kadison’s theorem for orthogonal projections (2002) and the second author’s result for operators with three-point spectrum (2013).
Wydawca
Rocznik
Tom
Strony
249--260
Opis fizyczny
Bibliogr. 13 poz., wykr.
Twórcy
autor
- Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, U.S.A.
autor
- Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, U.S.A.
Bibliografia
- [1] W. Arveson, Diagonals of normal operators with finite spectrum, Proc. Nat. Acad. Sci. USA 104 (2007), 1152–1158.
- [2] W. Arveson and R. Kadison, Diagonals of self-adjoint operators, in: Operator Theory, Operator Algebras, and Applications, Contemp. Math. 414, Amer. Math. Soc., Providence, RI, 2006, 247–263.
- [3] M. Bownik and J. Jasper, The Schur–Horn theorem for operators with finite spectrum, Trans. Amer. Math. Soc. 367 (2015), 5099–5140.
- [4] M. Bownik and J. Jasper, Spectra of frame operators with prescribed frame norms, in: Harmonic Analysis and Partial Differential Equations, Contemp. Math. 612, Amer. Math. Soc., Providence, RI, 2014, 65–79.
- [5] I. C. Gohberg and A. S. Markus, Some relations between eigenvalues and matrix elements of linear operators, Mat. Sb. (N.S.) 64 (1964), 481–496 (in Russian).
- [6] A. Horn, Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math. 76 (1954), 620–630.
- [7] J. Jasper, The Schur–Horn theorem for operators with three point spectrum, J. Funct. Anal. 265 (2013), 1494–1521.
- [8] R. Kadison, The Pythagorean theorem. I. The finite case, Proc. Nat. Acad. Sci. USA 99 (2002), 4178–4184.
- [9] R. Kadison, The Pythagorean theorem. II. The infinite discrete case, Proc. Nat. Acad. Sci. USA 99 (2002), 5217–5222.
- [10] V. Kaftal and G. Weiss, A survey on the interplay between arithmetic mean ideals, traces, lattices of operator ideals, and an infinite Schur–Horn majorization theorem, in: Hot Topics in Operator Theory, Theta Ser. Adv. Math. 9, Theta, Bucharest, 2008, 101–135.
- [11] V. Kaftal and G. Weiss, An infinite-dimensional Schur–Horn theorem and majorization theory, J. Funct. Anal. 259 (2010), 3115–3162.
- [12] A. Neumann, An infinite-dimensional version of the Schur–Horn convexity theorem, J. Funct. Anal. 161 (1999), 418–451.
- [13] I. Schur, Über eine Klasse von Mittelbildungen mit Anwendungen auf die Determinantentheorie, Sitzungsber. Berlin. Math. Ges. 22 (1923), 9–20.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9cf59d40-ab5c-4662-851d-549a39f415a4