Arkiv för Matematik

  • Ark. Mat.
  • Volume 29, Number 1-2 (1991), 73-81.

Extreme operator-valued continuous maps

R. Grz⇓ślewicz

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Abstract

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.

Article information

Source
Ark. Mat., Volume 29, Number 1-2 (1991), 73-81.

Dates
Received: 26 September 1986
Revised: 9 November 1989
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898031

Digital Object Identifier
doi:10.1007/BF02384332

Mathematical Reviews number (MathSciNet)
MR1115076

Rights
1991 © Institut Mittag-Leffler

Citation

Grz⇓ślewicz, R. Extreme operator-valued continuous maps. Ark. Mat. 29 (1991), no. 1-2, 73--81. doi:10.1007/BF02384332. https://projecteuclid.org/euclid.afm/1485898031


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