Faruk POLAT

7581

Order continuous operators on CD0(K, E) and CDw(K, E)-spaces

In [2], Alpay and Ercan characterized order continuous duals of spaces CD0(K, E) and CDw(K, E) where K is a compact Hausdorff space without isolated points and E is a Banach lattice. In this note, we generalize their results to an arbitrary Dedekind complete Banach lattice F, that is to say, we characterize order continuous operators on these spaces taking values in an arbitrary Dedekind complete Banach lattice F.Recall that a topological space is called basically disconnected if the closure of any Fσ -open set is open. A compact Hausdorff space that is basically disconnected will be referred to as a quasi-Stonean space. For a quasi-Stonean space K without isolated points, the following function spaces were introduced by Abramovichand Wickstead [1

Keywords:

CD0(K)-spaces, order continuous operators isometric lattice isomorphism,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

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