Fixräume regulärer operatoren und ein Korovkin-Satz |
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Authors: | Egon Scheffold |
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Institution: | Fachbereich Mathematik der Technischen Hochschule Darmstadt, BRD-6100 Darmstadt, West-Germany |
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Abstract: | S. J. Bernau has introduced the notion of an exchange subspace of an Lp-space and has shown that the range of a contractive linear projection on an Lp-space (1 ? p < ∞, p ≠ 2) is an exchange subspace. In the present paper we define this notion for real Banach lattices with order continuous norm and prove among other things that fixed spaces of special regular operators on these spaces are exchange subspaces. As application we give a Korovkin theorem for sequences of contractions on real Banach lattices with an uniformly monotone norm. |
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