2 results
Some results on various types of compactness of weak* Dunford–Pettis operators on Banach lattices
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- Journal:
- Canadian Mathematical Bulletin / Volume 67 / Issue 2 / June 2024
- Published online by Cambridge University Press:
- 23 October 2023, pp. 403-414
- Print publication:
- June 2024
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We study the relationship between weak* Dunford–Pettis and weakly (resp. M-weakly, order weakly, almost M-weakly, and almost L-weakly) operators on Banach lattices. The following is one of the major results dealing with this matter: If E and F are Banach lattices such that F is Dedekind
$\sigma $-complete, then each positive weak* Dunford–Pettis operator 
$T:E\rightarrow F$ is weakly compact if and only if one of the following assertions is valid: (a) the norms of 
$E^{\prime }$ and F are order continuous; (b) E is reflexive; and (c) F is reflexive.
The Duality Problem for the Class of AM-Compact Operators on Banach Lattices
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- Journal:
- Canadian Mathematical Bulletin / Volume 51 / Issue 1 / 01 March 2008
- Published online by Cambridge University Press:
- 20 November 2018, pp. 15-20
- Print publication:
- 01 March 2008
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We prove the converse of a theorem of Zaanen about the duality problem of positive
$\text{AM}$-compact operators.
