Abstract
Let π,π,πβ²β[1,β]
, πβ²β€π
. Several new characterizations of locally convex spaces with the sequential DunfordβPettis property of order (π,π)
are given. We introduce and thoroughly study the sequential DunfordβPettis* property of order (π,π)
of locally convex spaces (in the realm of Banach spaces, the sequential π·πβ(π,β)
property coincides with the well-known π·πβπ
property). Being motivated by the coarse p-π·πβ
property and the p-DunfordβPettis relatively compact property for Banach spaces, we define and study the coarse sequential π·πβ(π,π)
property, the coarse π·πβπ
property and the p-DunfordβPettis sequentially compact property of order (πβ²,π)
in the class of all locally convex spaces.
, πβ²β€π
. Several new characterizations of locally convex spaces with the sequential DunfordβPettis property of order (π,π)
are given. We introduce and thoroughly study the sequential DunfordβPettis* property of order (π,π)
of locally convex spaces (in the realm of Banach spaces, the sequential π·πβ(π,β)
property coincides with the well-known π·πβπ
property). Being motivated by the coarse p-π·πβ
property and the p-DunfordβPettis relatively compact property for Banach spaces, we define and study the coarse sequential π·πβ(π,π)
property, the coarse π·πβπ
property and the p-DunfordβPettis sequentially compact property of order (πβ²,π)
in the class of all locally convex spaces.
Original language | English |
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Number of pages | 28 |
Journal | Axioms |
Volume | 13 (7) |
Issue number | 491 |
DOIs | |
State | Published - 2024 |