Order continuous operators on $CD _0$(K,E) and $CD _omega$(K,E)-spaces

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

In [2], Alpay and Ercan characterized order continuous duals of spaces $CD _0$(K,E)and $CD _omega$(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 .

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[1] Abramovich, Y. A. and Wickstead A. W.: Remarkable classes of unital AM-spaces, J. of Math. Analysis and Appl. 180 (1993), 398-411.
[2] Alpay, S ¸. and Ercan, Z.: $CD _0$(K,E) and $CD _omega$(K,E) -spaces as Banach lattices, Positivity 4 (2000), 213-225.
[3] Aliprantis, C. D. and Burkinshaw, O.: Positive Operators, Academic Press, Inc.(1985).