Abstract
AbstractA non-empty set of operators $$\mathcal {M}$$
M
is reflexive if an operator T is in $$\mathcal {M}$$
M
if and only if $$Tx\in \overline{\mathcal {M} x}$$
T
x
∈
M
x
¯
, for all vectors x. In this paper, we study the reflexivity of finite-dimensional sets of operators. We introduce the class of flat sets of operators and prove several results related to the reflexivity of these sets; in particular, we show that the convex hull of three (or fewer) operators is reflexive.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis