1. CMB 2005 (vol 48 pp. 267)
 Rodman, Leiba; Å emrl, Peter; Sourour, Ahmed R.

Continuous Adjacency Preserving Maps on Real Matrices
It is proved that every adjacency preserving continuous map
on the vector space of real matrices of fixed size, is either a
bijective affine tranformation
of the form $ A \mapsto PAQ+R$, possibly followed by the transposition if
the matrices are of square size, or its range is contained
in a linear subspace consisting of matrices of rank at most one
translated by some matrix $R$. The result
extends previously known
theorems where the map was assumed to be also injective.
Keywords:adjacency of matrices, continuous preservers, affine transformations Categories:15A03, 15A04. 

2. CMB 2003 (vol 46 pp. 54)
 Cheung, WaiShun; Li, ChiKwong

Linear Maps Transforming the Unitary Group
Let $U(n)$ be the group of $n\times n$ unitary matrices. We show that if
$\phi$ is a linear transformation sending $U(n)$ into $U(m)$, then $m$ is
a multiple of $n$, and $\phi$ has the form
$$
A \mapsto V[(A\otimes I_s)\oplus (A^t \otimes I_{r})]W
$$
for some $V, W \in U(m)$. From this result, one easily deduces the
characterization of linear operators that map $U(n)$ into itself obtained
by Marcus. Further generalization of the main theorem is also discussed.
Keywords:linear map, unitary group, general linear group Category:15A04 

3. CMB 2001 (vol 44 pp. 270)
 Cheung, WaiShun; Li, ChiKwong

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 
