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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the extreme points of the interval between two operators


Author: Francis J. Narcowich
Journal: Proc. Amer. Math. Soc. 67 (1977), 84-86
MSC: Primary 47D20; Secondary 47A99
DOI: https://doi.org/10.1090/S0002-9939-1977-0454737-6
MathSciNet review: 0454737
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Abstract: Given that A, B are operators on a complex Hilbert space, and that $ B - A$ is nonnegative, the interval between A and B consists of every operator, G, such that both $ B - G$ and $ G - A$ are nonnegative. The extreme points of such an interval are exhibited and the interval is shown to be the closure of the convex hull of these extreme points in the weak-operator topology.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0454737-6
Keywords: Interval between two operators, extreme points, convex hull
Article copyright: © Copyright 1977 American Mathematical Society