Locally convex spaces with sequential Dunford-Pettis type properties

Research output: Contribution to journal β€Ί Article β€Ί peer-review

Abstract

Let 𝑝,π‘ž,π‘žβ€²βˆˆ[1,∞]
, π‘žβ€²β‰€π‘ž
. Several new characterizations of locally convex spaces with the sequential Dunford–Pettis property of order (𝑝,π‘ž)
are given. We introduce and thoroughly study the sequential Dunford–Pettis* property of order (𝑝,π‘ž)
of locally convex spaces (in the realm of Banach spaces, the sequential π·π‘ƒβˆ—(𝑝,∞)
property coincides with the well-known π·π‘ƒβˆ—π‘
property). Being motivated by the coarse p-π·π‘ƒβˆ—
property and the p-Dunford–Pettis relatively compact property for Banach spaces, we define and study the coarse sequential π·π‘ƒβˆ—(𝑝,π‘ž)
property, the coarse π·π‘ƒβˆ—π‘
property and the p-Dunford–Pettis sequentially compact property of order (π‘žβ€²,π‘ž)
in the class of all locally convex spaces.
Original languageEnglish
Number of pages28
JournalAxioms
Volume13 (7)
Issue number491
DOIs
StatePublished - 2024

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