Geodesic
Regular vector lattices of continuous functions and Korovkin-type theorems—Part II
Francesco Altomare1 ; Mirella Cappelletti Montano1
1Department of Mathematics University of Bari Campus Universitario Via E. Orabona, 4 70125 Bari, Italy
Studia Mathematica, Tome 172 (2006) no. 1, pp. 69-90
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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By applying the results of the first part of the paper, we establish some Korovkin-type theorems for continuous positive linear operators in the setting of regular vector lattices of continuous functions. Moreover, we present simple methods to construct Korovkin subspaces for finitely defined operators and for the identity operator and we determine those classes of operators which admit finite-dimensional Korovkin subspaces. Finally, we give a Korovkin-type theorem for continuous positive projections.
DOI : 10.4064/sm172-1-4
Keywords: applying results first part paper establish korovkin type theorems continuous positive linear operators setting regular vector lattices continuous functions moreover present simple methods construct korovkin subspaces finitely defined operators identity operator determine those classes operators which admit finite dimensional korovkin subspaces finally korovkin type theorem continuous positive projections

Francesco Altomare  1   ; Mirella Cappelletti Montano  1

1 Department of Mathematics University of Bari Campus Universitario Via E. Orabona, 4 70125 Bari, Italy 
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Francesco Altomare; Mirella Cappelletti Montano. Regular vector lattices of continuous functions
 and Korovkin-type theorems—Part II. Studia Mathematica, Tome 172 (2006) no. 1, pp. 69-90. doi: 10.4064/sm172-1-4

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