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Disjoint p$p$‐convergent operators and their adjoints
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AbstractFirst, we give conditions on a Banach lattice so that an operator from to any Banach space is disjoint ‐convergent if and only if is almost Dunford–Pettis. Then, we study when adjoints of positive operators between Banach lattices are disjoint ‐convergent. For instance, we prove that the following conditions are equivalent for all Banach lattices and : (i) a positive operator is almost weak ‐convergent if and only if is disjoint ‐convergent; (ii) has order continuous norm or has the positive Schur property of order . Very recent results are improved, examples are given and applications of the main results are provided.
Title: Disjoint p$p$‐convergent operators and their adjoints
Description:
AbstractFirst, we give conditions on a Banach lattice so that an operator from to any Banach space is disjoint ‐convergent if and only if is almost Dunford–Pettis.
Then, we study when adjoints of positive operators between Banach lattices are disjoint ‐convergent.
For instance, we prove that the following conditions are equivalent for all Banach lattices and : (i) a positive operator is almost weak ‐convergent if and only if is disjoint ‐convergent; (ii) has order continuous norm or has the positive Schur property of order .
Very recent results are improved, examples are given and applications of the main results are provided.
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