Abstract
A bounded linear operatorT is a numerical contraction if and only if there exists a selfadjoint contractionZ such that\(\left[ {\begin{array}{*{20}c} {I + Z} & T \\ {T^* } & {I - Z} \\ \end{array} } \right] \geqslant 0\). The aim of the present paper is to study the structure of the coreZ(T) of all selfadjoint contractions satisfying the above inequality. Especially we consider several conditions for thatZ(T) is a single-point set. By using this argument we shall characterize extreme points of the set of all numerical contractions. Moreover we shall give effective sufficient conditions for extreme points.
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