On the extreme points of the interval between two operators
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- by Francis J. Narcowich PDF
- Proc. Amer. Math. Soc. 67 (1977), 84-86 Request permission
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.References
- R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413–415. MR 203464, DOI 10.1090/S0002-9939-1966-0203464-1 N. Dunford and J. T. Schwartz, Linear operators. Part I, Interscience, New York, 1967.
- Francis J. Narcowich, $R$-operators. II. On the approximation of certain operator-valued analytic functions and the Hermitian moment problem, Indiana Univ. Math. J. 26 (1977), no. 3, 483–513. MR 457739, DOI 10.1512/iumj.1977.26.26038
- Shôichirô Sakai, $C^*$-algebras and $W^*$-algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York-Heidelberg, 1971. MR 0442701
Additional Information
- © Copyright 1977 American Mathematical Society
- 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