On weak-star p-convergent operators
| Autor: | Fourie, Jan H., Zeekoei, Elroy D. |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Quaestiones Mathematicae; Vol 40, No 5 (2017); 563-579 |
| ISSN: | 1607-3606 1727-933X |
| Popis: | The purpose of this article is to introduce and study the notion of "weak*p-convergent operator". We discuss the relationship between the weak* p-convergent operators and the p-convergent operators, a class of operators that was introduced in the paper [4] and which plays an important role in the study of the DP* -property of order p (in the paper [14]). Some new characterizations of Banach spaces with the DP* -property of order p are obtained, the p-Gelfand-Phillips property is introduced and the behaviour of weak* p-convergent operators on Banach spaces with this property (with focus on Banach lattices with the p-Gelfand-Phillips property) is investigated. In the last section of this paper, we consider the domination properties of positive p-convergent and positive weak* p-convergent operators on Banach lattices.Keywords: p-Convergent operator, weak* p-convergent operator, DP*-property of order p, p-Gelfand-Phillips property, domination property on Banach lattices |
| Databáze: | OpenAIRE |
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