Markov operators, peak points, and Choquet points
HTML articles powered by AMS MathViewer
- by Robert E. Atalla PDF
- Proc. Amer. Math. Soc. 41 (1973), 103-109 Request permission
Abstract:
We deal with conditions on a closed subspace $L$ of $C(X)$ under which weak peak points are equivalent with Choquet points. If $L$ satisfies a strengthened form of this equivalence (’weak peak sets = Choquet sets’—definitions are given below), then for any image of $L$ under a Markov projection, weak peak points and Choquet points are equivalent. Conditions under which $L$ satisfies the strengthened equivalence include (i) $L$ interpolates its Shilov boundary, and (ii) $L$ is the space of fixed points of a Markov operator $T$ on $C(X)$, where $T$ is in an appropriate sense concentrated on the Shilov boundary of $L$.References
- Robert E. Atalla, On the multiplicative behavior of regular matrices, Proc. Amer. Math. Soc. 26 (1970), 437–446. MR 271752, DOI 10.1090/S0002-9939-1970-0271752-X
- Gerald M. Leibowitz, Lectures on complex function algebras, Scott, Foresman & Co., Glenview, Ill., 1970. MR 0428042
- S. P. Lloyd, On certain projections in spaces of continuous functions, Pacific J. Math. 13 (1963), 171–175. MR 152873
- Robert R. Phelps, Lectures on Choquet’s theorem, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0193470
- Zbigniew Semadeni, Banach spaces of continuous functions. Vol. I, Monografie Matematyczne, Tom 55, PWN—Polish Scientific Publishers, Warsaw, 1971. MR 0296671
- Robert Sine, Geometric theory of a single Markov operator, Pacific J. Math. 27 (1968), 155–166. MR 240281
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 103-109
- MSC: Primary 46E25; Secondary 47B99
- DOI: https://doi.org/10.1090/S0002-9939-1973-0318861-7
- MathSciNet review: 0318861