Proyecciones Journal of Mathematics
Vol. 30, N° 1, pp. 77-90, May 2011.
Universidad Católica del Norte
Antofagasta - Chile


Numerical range of a pair of strictly upper triangular matrices


Wen Yan

Tuskegee University, U. S. A.


Correspondencia a:

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Abstract

Given two strictly upper triangular matrices X, Y ∈ C_m×m, we study the range W_Y (X) = {trnXn^-1Y* : n ∈ N}, where N is the group of unit upper triangular matrices in C_m×m. We prove that it is either a point or the whole complex plane. We characterize when it is a point. We also obtain some convexity result for a similar range, where N is replaced by any ball of C^k (k = m(m - 1)/2) embedded in N , m = 4.

2000 Mathematics Subject Classification : Primary 15A60.

Key Words and Phrases : Numerical range, unit upper triangular matrices, strictly upper triangular matrices.

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Wen Yan
Department of Mathematics
Tuskegee University
AL 36088
U. S. A.
e-mail : wyliamg@gmail.com

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Received : January 2011. Accepted : March 2011