Extreme operator-valued continuous maps

R. Grz⇓ślewicz Institute of Mathematics, Technical University

TBD mathscidoc:1701.332743

Arkiv for Matematik, 29, (1), 73-81, 1986.9
Let ℒ($H$) denote the space of operators on a Hilbert space$H$. We show that the extreme points of the unit ball of the space of continuous functions$C(K, ℒ(H))$($K$-compact Hausdorff) are precisely the functions with extremal values. We show also that these extreme points are (a) strongly exposed if and only if dim$H$<∞ and card$K$<∞, (b) exposed if and only if$H$is separable and$K$carries a strictly positive measure.
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  title={Extreme operator-valued continuous maps},
  author={R. Grz⇓ślewicz},
  booktitle={Arkiv for Matematik},
R. Grz⇓ślewicz. Extreme operator-valued continuous maps. 1986. Vol. 29. In Arkiv for Matematik. pp.73-81. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203534490675552.
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