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1. CMB 2001 (vol 44 pp. 270)

Cheung, Wai-Shun; Li, Chi-Kwong
 Linear Operators Preserving Generalized Numerical Ranges and Radii on Certain Triangular Algebras of Matrices Let $c = (c_1, \dots, c_n)$ be such that $c_1 \ge \cdots \ge c_n$. The $c$-numerical range of an $n \times n$ matrix $A$ is defined by $$W_c(A) = \Bigl\{ \sum_{j=1}^n c_j (Ax_j,x_j) : \{x_1, \dots, x_n\} \text{ an orthonormal basis for } \IC^n \Bigr\},$$ and the $c$-numerical radius of $A$ is defined by $r_c (A) = \max \{|z| : z \in W_c (A)\}$. We determine the structure of those linear operators $\phi$ on algebras of block triangular matrices, satisfying $$W_c \bigl( \phi(A) \bigr) = W_c (A) \text{ for all } A \quad \text{or} \quad r_c \bigl( \phi(A) \bigr) = r_c (A) \text{ for all } A.$$ Keywords:linear operator, numerical range (radius), block triangular matricesCategories:15A04, 15A60, 47B49
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