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1. CMB 2011 (vol 55 pp. 208)
Abelian Gradings on Upper Block Triangular Matrices Let $G$ be an arbitrary finite abelian group. We describe all
possible $G$-gradings on upper block triangular matrix algebras
over an algebraically closed field of characteristic zero.
Keywords:gradings, upper block triangular matrices Category:16W50 |
2. CMB 2001 (vol 44 pp. 270)
Linear Operators Preserving Generalized Numerical Ranges and Radii on Certain Triangular Algebras of Matrices |
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 matrices Categories:15A04, 15A60, 47B49 |