Abstract view
Linear Operators Preserving Generalized Numerical Ranges and Radii on Certain Triangular Algebras of Matrices


Published:20010901
Printed: Sep 2001
WaiShun Cheung
ChiKwong Li
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Abstract
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
$$
W_c \bigl( \phi(A) \bigr) = W_c (A) \text{ for all } A \quad \text{or}
\quad r_c \bigl( \phi(A) \bigr) = r_c (A) \text{ for all } A.
$$
MSC Classifications: 
15A04, 15A60, 47B49 show english descriptions
Linear transformations, semilinear transformations Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05] Transformers, preservers (operators on spaces of operators)
15A04  Linear transformations, semilinear transformations 15A60  Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05] 47B49  Transformers, preservers (operators on spaces of operators)
