Ideal Properties of Regular Operators between Banach Lati ’ Ices
نویسنده
چکیده
Suppose E and F are Banach lattices such that E* and F have order-continuous norms. In [4] Dodds and Fremlin (cf. also [1]) showed that if T: E F is a positive compact operator and 0 < S < T then S is also compact. Aliprantis and Burkinshaw [1] showed by examples that the hypotheses on E and F are necessary. In [2] they asked whether a similar result is true for Dunford-Pettis operators, under the same hypotheses on E and F. In this paper we give a positive answer to the question of Aliprantis and Burkinshaw. However, after the initial preparation of the paper we learned of the work of W. Haid [6] who also had answered the question in the form stated a little before our work (see also de Pagter [9]). Haid’s theorem is:
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