Page 129 - Textos de Matemática Vol. 44

CONNECTEDNESS, HESSIANS AND GENERALIZED NUMERICAL RANGES 119
[18] C. K. Li, C-numerical ranges and C-numerical radii, Linear Multilinear Algebra 37 (1994), 51–82.
[19] C. K. Li and T. Y. Tam, Numerical ranges arising from simple Lie algebras, Canad. J. Math. 52 (2000), 141–171.
[20] M. Liao, L´evy Processes in Lie Groups, Cambridge University Press, 2004.
[21] A. Markus and T. Y. Tam, Connectedness of some fibres on a compact connected Lie
group, Linear Multilinear Algebra 59 (2011), 1121–1126.
[22] J. Milnor, Morse theory, Princeton University Press, N.J. 1963.
[23] Y. T. Poon, Another proof of a result of Westwick, Linear and Multilinear Algebra 9
(1980), 35–37.
[24] M. Ra¨ıs, Remarques sur un theoreme de R. Westwick, unpublished manuscript.
[25] T.Y. Tam, On the shape of numerical ranges associated with Lie groups, Taiwanese J.
Math. 5 (2001), 497–506.
[26] , Convexity of generalized numerical range associated with a compact Lie group,
J. Austral. Math. Soc. 72 (2002), 57–66.
[27] O. Toeplitz, Das algebraische Analogon zu einem Satze von Fej´er, Math. Z. 2 (1918),
187–197.
[28] V. S. Varadarajan, The Method of Stationary Phase and Applications to Geometry and
Analysis on Lie Groups, Book Chapter in Algebraic and Analytic Methods in Represen-
tation Theory, Academic Press, 1997, 167–242.
[29] R. Westwick, A theorem on numerical range, Linear and Multilinear Algebra 2 (1975),
311–315.
(X. Liu) Department of Mathematics,The University of Tennessee at Chattanooga, 415 EMCS Building, 615 McCallie Avenue, Chattanooga, TN 37403, USA
E-mail address: Roy-Liu@utc.edu
(T.-Y. Tam) Department of Mathematics and Statistics, 221 Parker Hall, Auburn University, Auburn, AL 36849-5310, USA
E-mail address: tamtiny@auburn.edu