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Research Article

Convexity of the orbit-closed C-numerical range and majorization

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Pages 4707-4750 | Received 25 Aug 2020, Accepted 29 Jan 2021, Published online: 27 Apr 2021

References

  • Toeplitz O. Das algebraische analogon zu einem satze von Fejér. Math Z. 1918;2(1-2):187–197.
  • Hausdorff F. Der wertvorrat einer bilinearform. Math Z. 1919;3(1):314–316.
  • Davis C. The Toeplitz-Hausdorff theorem explained. Can Math Bull. 1971;14:245–246.
  • Halmos PR. Numerical ranges and normal dilations. Acta Sci Math. 1964;25:1–5.
  • Berger CA. Normal dilations [dissertation]. Cornell University, Ithaca, New York; 1963.
  • Fillmore PA, Williams JP. Some convexity theorems for matrices. Glasgow Math J. 1971;12:110–117.
  • Westwick R. A theorem on numerical range. Linear Multilinear Algebra. 1975;2:311–315.
  • Goldberg M, Straus EG. Elementary inclusion relations for generalized numerical ranges. Linear Algebra Appl. 1977;18:1–24.
  • Li CK. C-numerical ranges and C-numerical radii. Linear Multilinear Algebra. 1994;37(1-3):51–82.
  • Au-Yeung YH, Tsing NK. A conjecture of marcus on the generalized numerical range. Linear Multilinear Algebra. 1983;14:235–239.
  • Cheung WS, Tsing NK. The C-numerical range of matrices is star-shaped. Linear Multilinear Algebra. 1996;41(3):245–250.
  • Marcus M. Some combinatorial aspects of numerical range. Ann NY Acad Sci. 1979;319(1):368–376.
  • Dirr G. The C-numerical range in infinite dimensions. Linear Multilinear Algebra. 2020;68(4):652–678.
  • Dykema K, Skoufranis P. Numerical ranges in II1 factors. Proc Edinb Math Soc, II Ser. 2017;61(1):31–55.
  • Poon YT. Another proof of a result of Westwick. Linear Multilinear Algebra. 1980;9:35–37.
  • Birkhoff G. Three observations on linear algebra. Univ Nac Tucumán Rev A. 1946;5:147–151.
  • Arveson W, Kadison RV. Diagonals of self-adjoint operators. In: Han D, Jorgensen PE, Larson DR, editors. Operator theory, operator algebras, and applications. Providence, RI: American Mathematica Society; 2006. p. 247–263. (Contemp. Math.; vol. 414).
  • Kaftal V, Weiss G. An infinite dimensional Schur–Horn theorem and majorization theory. J Funct Anal. 2010;259(12):3115–3162.
  • Loreaux J. Diagonals of operators [dissertation]. University of Cincinnati, Cincinnati, Ohio; 2016.
  • Gellar R, Page L. Limits of unitarily equivalent normal operators. Duke Math J. 1974;41:319–322.
  • Voiculescu D. A non-commutative Weyl-von Neumann theorem. Rev Roum Math Pures Appl. 1976;21(1):97–113.
  • Hiai F, Nakamura Y. Closed convex hulls of unitary orbits in von Neumann algebras. Trans Am Math Soc. 1991;323(1):1–38.
  • Chu CH. A note on scattered C*-algebras and the Radon-Nikodym property. J Lond Math Soc II Ser. 1981;24:533–536.
  • Phelps RR. Dentability and extreme points in Banach spaces. J Funct Anal. 1974;17:78–90.
  • Chan JT, Li CK, Poon YT. Closedness of the k-numerical range. Linear Multilinear Algebra. 2020;1–9. DOI:10.1080/03081087.2020.1790483.
  • Lancaster J. The boundary of the numerical range. Proc Am Math Soc. 1975;49:393.
  • de Barra G, Giles JR, Sims B. On the numerical range of compact operators on Hilbert spaces. J Lond Math Soc II Ser. 1972;5:704–706.
  • Li CK, Poon YT. Some results on the c-numerical range. In: Five decades as a mathematician and educator. On the 80th birthday of Professor Yung-Chow Wong. Singapore: World Scientific; 1995. p. 247–258.
  • Fan P, Fong CK. Which operators are the self-commutators of compact operators?. Proc Am Math Soc 1980;80:58–60.
  • Kippenhahn R. Über den wertevorrat einer matrix. Math Nachr. 1951;6:193–228.
  • Kippenhahn R. Über den wertevorrat einer matrix. Linear Multilinear Algebra. 2008;56(1-2):185–225.
  • Johnson CR. Numerical determination of the field of values of a general complex matrix. SIAM J Numer Anal. 1978;15:595–602.
  • Marshall AW, Olkin I, Arnold BC. Inequalities: theory of majorization and its applications. 2nd ed. New York (NY): Springer; 2011.
  • Blackadar B. Operator algebras. Theory of C-algebras and von Neumann algebras. Berlin: Springer; 2006.
  • Makarov KA, Seelmann A. The length metric on the set of orthogonal projections and new estimates in the subspace perturbation problem. J Reine Angew Math. 2015;708:1–15.
  • Schur I. Über eine klasse von mittelbildungen mit anwendungen auf der determinantentheorie. Sitzungsber Berliner Mat Ges. 1923;22:9–29.
  • Horn A. Doubly stochastic matrices and the diagonal of a rotation matrix. Am J Math. 1954;76:620–630.
  • Radjavi H, Rosenthal P. Simultaneous triangularization. New York (NY): Springer; 2000.
  • Loreaux J, Weiss G. On diagonals of operators: selfadjoint, normal and other classes. In: Operator Theory: Themes and Variations – Conference Proceedings, Timioara, July 2–6, 2018; Theta Foundation, Bucharest, Romania; 2020. p. 193–214.
  • Loreaux J, Weiss G. Majorization and a Schur–Horn theorem for positive compact operators, the nonzero kernel case. J Funct Anal. 2015;268(3):703–731.

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