Abstract

A non-empty set of operators mathcal {M} is reflexive if an operator T is in mathcal {M} if and only if Txin overline{mathcal {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.

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