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Original Articles

Higher rank numerical ranges of Jordan-like matrices

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Pages 807-826 | Received 11 Aug 2019, Accepted 14 Oct 2019, Published online: 30 Oct 2019

References

  • Ando T. Structure of operators with numerical radius one. Acta Sci Math (Szeged). 1973;34:11–15.
  • Bickel K, Gorkin P. Compressions of the shift on the bidisk and their numerical ranges. J Operator Theory. 2018;79(1):225–265.
  • Gau H-L, Li C-K. C∗-isomorphisms, Jordan isomorphisms, and numerical range preserving maps. Proc Amer Math Soc. 2007;135(9):2907–2914.
  • Kato T. Perturbation theory for linear operators. Classics in Mathematics. Berlin: Springer-Verlag; 1995. Reprint of the 1980 edition.
  • Kribs DW, Pasieka A, Laforest M, et al. Research problems on numerical ranges in quantum computing. Linear Multilinear Algebra. 2009;57(5):491–502.
  • Li C-K, Sze N-S. Canonical forms, higher rank numerical ranges, totally isotropic subspaces, and matrix equations. Proc Am Math Soc. 2008;136(9):3013–3023.
  • Li C-K, Tam B-S, Wu PY. The numerical range of a nonnegative matrix. Linear Algebra Appl. 2002;350:1–23.
  • Li C-K. Inequalities relating norms invariant under unitary similarities. Linear Multi Algebra. 1991;29(3–4):155–167.
  • Spijker MN. Numerical ranges and stability estimates. Appl Numer Math. 1993;13(1–3):241–249.
  • Horn R, Charles RJ. Topics in matrix analysis. Cambridge: Cambridge University Press; 1994.
  • Halmos PR. A Hilbert space problem book. Vol. 19. 2nd ed. Graduate Texts in Mathematics. New York: Springer-Verlag; 1982. Encyclopedia of Mathematics and its Applications, 17.
  • Choi M-D, Kribs DW, Życzkowski K. Higher-rank numerical ranges and compression problems. Linear Algebra Appl. 2006;418(2–3):828–839.
  • Woerdeman HJ. The higher rank numerical range is convex. Linear Multilinear Algebra. 2008;56(12):65–67.
  • Choi M-D, Holbrook JA, Kribs DW, et al. Higher-rank numerical ranges of unitary and normal matrices. Oper Matrices. 2007;1(3):409–426.
  • Gaaya H. On the higher rank numerical range of the shift operator. J Math Sci Adv Appl. 2012;13(1):1–19.
  • Adam M, Aretaki A, Spitkovsky IM. Elliptical higher rank numerical range of some Toeplitz matrices. Linear Algebra Appl. 2018;549:256–275.
  • Chien M-T, Nakazato H. The boundary of higher rank numerical ranges. Linear Algebra Appl. 2011;435(11):2971–2985.
  • Haagerup U, de la Harpe P. The numerical radius of a nilpotent operator on a Hilbert space. Proc Amer Math Soc. 1992;115(2):371–379.
  • de Lagrange J-L. Recherches sur la nature et la propagation du son. Miscellanea Taurinensia. 1759;1:39–148.
  • Chang C-T, Gau H-L, Wang K-Z. Equality of higher-rank numerical ranges of matrices. Linear Multilinear Algebra. 2014;62(5):626–638.
  • Donoghue WF. On the numerical range of a bounded operator. Michigan Math J. 1957;4(3):261–263.
  • Li C-K, Poon Y-T, Sze N-S. Condition for the higher rank numerical range to be non-empty. Linear Multilinear Algebra. 2009;57(4):365–368.
  • Tam B-S, Yang S. On matrices whose numerical ranges have circular or weak circular symmetry. Linear Algebra Appl. 1999;302/303:193–221. Special issue dedicated to Hans Schneider (Madison, WI, 1998).
  • Wu PY. Numerical ranges as circular discs. Appl Math Lett. 2011;24(12):2115–2117.
  • Gau H-L, Wu P. Anderson's theorem for compact operators. Proc Am Math Soc. 2006;134(11):3159–3162.
  • Gau H-L, Wu PY. Higher-rank numerical ranges and Kippenhahn polynomials. Linear Algebra Appl. 2013;438(7):3054–3061.

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