Lattice homomorphism — korovkin type inequalities for vector valued functions

Abstract

Considered here is the space of continuous functions from a compact and convex subset of a normed vector space into an abstract Banach lattice. Also considered are lattice homomorphisms from the above space into itself or into the associated space of vector valued bounded functions. The uniform convergence of such operators to the unit operator with rates is mainly studied in this article. The produced quantitative results are inequalities which engage the modulus of continuity of the involved continuous function or of its higher order Fréchet derivative. © 1997 by the University of Notre Dame. All rights reserved.

Publication Title

Hokkaido Mathematical Journal

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