Regular vector lattices of continuous functions and Korovkin-type theorems-Part I

• Autorzy: Francesco Altomare , Mirella Cappelletti Montano
• Języki publikacji: EN

Abstrakty

EN

We introduce and study a new class of locally convex vector lattices of continuous functions on a locally compact Hausdorff space, which we call regular vector lattices. We investigate some general properties of these spaces and of the subspaces of so-called generalized affine functions. Moreover, we present some Korovkin-type theorems for continuous positive linear operators; in particular, we study Korovkin subspaces for finitely defined operators, for the identity operator and for positive projections.
Due to its length, the paper is split up into two parts of distinct character; in this first part, we introduce the class of regular vector lattices, we prove an integral representation theorem for continuous positive linear forms and we study some enveloping functions related to a continuous positive operator, together with the corresponding space of generalized affine functions. Finally, we obtain a Stone-Weierstrass type theorem.
In the second part, which will appear in the same journal, we will present some Korovkin-type theorems, together with some applications.

Kategorie tematyczne

• 46E05: Lattices of continuous, differentiable or analytic functions
• 46E99: None of the above, but in this section
• 46E10: Topological linear spaces of continuous, differentiable or analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 171
• Numer: 3
• Strony: 239-260

Daty

wydano

2005

Twórcy

autor

Francesco Altomare

• Department of Mathematics, University of Bari, Campus Universitario, Via E. Orabona, 4, 70125 Bari, Italy

autor

Mirella Cappelletti Montano

• Department of Mathematics, University of Bari, Campus Universitario, Via E. Orabona, 4, 70125 Bari, Italy

Identyfikatory

DOI

10.4064/sm171-3-3