Extreme points in the set of normal spectral approximants.

*(English)*Zbl 0802.47012Summary: The discussion of normal spectral approximation in a unital \(C^*\)- algebra is continued. For the approximation by positive or self-adjoint elements and by positive contractions in the \(C^*\)-norm as well as in a second norm the extreme points of the convex set of all approximants are studied. The main purpose of this paper is to develop sufficient conditions for an approximant to be such an extreme point. As an application many extreme points for the approximation of normal elements are constructed. Moreover for the approximation in the \(C^*\)-algebra of all bounded linear operators on a complex Hilbert space the number of extreme points is completely determined.

##### MSC:

47A58 | Linear operator approximation theory |

41A35 | Approximation by operators (in particular, by integral operators) |

41A36 | Approximation by positive operators |

47L07 | Convex sets and cones of operators |