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H-joint numerical ranges

  • Chi-Kwong Li (a1) and Leiba Rodman (a1)

Abstract

The notion of the joint numerical range of several linear operators with respect to a sesquilinear form is introduced. Geometrical properties of the joint numerical range are studied, in particular, convexity and angle points, in connection with the algebraic properties of the operators. The main focus is on the finite dimensional case.

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References

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[1]Au-Yeung, Y.H. and Tsing, N.K., ‘An extension of the Hausdorff-Toeplitz theorem on the numerical range’, Proc. Amer. Math. Soc. 89 (1983), 215218.
[2]Binding, P. and Li, C.K., ‘Joint numerical ranges of Hermitian matrices and simultaneous diagonalization’, Linear Algebra Appl. 151 (1991), 157168.
[3]Donoghue, W.F. Jr., ‘On the numerical range of a bounded operator’, Michigan Math. J. 4 (1957), 261263.
[4]Fan, M.K.H. and Tits, A.L., ‘m-form numerical range and the computation of the structured singular value’, IEEE Trans. Automat. Control 33 (1988), 284289.
[5]Li, C.K., ‘A simple proof of the elliptical range theorem’, Proc. Amer. Math. Soc. 124 (1996), 19851986.
[6]Li, C.K., ‘The c-spectral, c-radial and c-convex matrices’, Linear and Multilinear Algebra 20 (1986), 515.
[7]Li, C.K. and Poon, Y.T., ‘Convexity of the joint numerical range’, SIAM J. Matrix Anal. Appl. 21 (2000), 668678.
[8]Li, C.K. and Rodman, L., ‘Remarks on numerical ranges of operators in spaces with an indefinite metric’, Proc. Amer. Math. Soc. 126 (1998), 973982.
[9]Li, C.K. and Tam, T.Y., ‘Numerical range arising from simple Lie algebras’, Canad. J. Math. 52 (2000), 141171.
[10]Li, C.K., Tsing, N.K. and Uhlig, F., ‘Numerical range of an operator on an indefinite inner product space’, Electron. J. Linear Algebra 1 (1996), 117.
[11]Marcus, M. and Filippenko, I., ‘Nondifferentiable boundary points of higher numerical range’, Linear Algebra Appl. 21 (1978), 217232.
[12]Poon, Y.T., ‘On the convex hull of the multiform numerical range’, Linear and Multilinear Algebra 37 (1994), 221223.
[13]Poon, Y.T., ‘Generalized numerical ranges, joint positive definiteness and multiple eigen-values’, Proc. Amer. Math. Soc. 125 (1997), 16251634.
[14]Wang, J.-C., Fan, M.K.H. and Tits, A.L., ‘Structured singular value and geometry of the m-form numerical range’, in Linear circuits, systems and signal processing: theory and application (Phoenix, AZ, 1987), (North-Holland, Amsterdam, 1988), pp. 609615.
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H-joint numerical ranges

  • Chi-Kwong Li (a1) and Leiba Rodman (a1)

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