Barrelled Weakly Köthe–Orlicz Summable Sequence Spaces

Issam Aboutaib, Janusz Brzdęk () and Lahbib Oubbi
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Issam Aboutaib: Laboratory LMSA, Department of Mathematics, Faculty of Sciences, Mohammed V University in Rabat, Avenue Ibn Battouta 4, Rabat 10108, Morocco
Janusz Brzdęk: Faculty of Applied Mathematics, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland
Lahbib Oubbi: Department of Mathematics, Ecole Normale Superieure, Mohammed V University in Rabat, Avenue Mohamed Bel Hassan El Ouazzani, Takaddoum, Rabat 10105, Morocco

Mathematics, 2023, vol. 12, issue 1, 1-16

Abstract: Let E be a Hausdorff locally convex space. We investigate the space Λ φ [ E ] of weakly Köthe–Orlicz summable sequences in E with respect to an Orlicz function φ and a perfect sequence space Λ . We endow Λ φ [ E ] with a Hausdorff locally convex topology and determine the continuous dual of the so-obtained space in terms of strongly Köthe–Orlicz summable sequences from the dual space E ′ of E . Next, we give necessary and sufficient conditions for Λ φ [ E ] to be barrelled or quasi-barrelled. This contributes to the understanding of different spaces of vector-valued sequences and their topological properties.

Keywords: summable sequences; vector-valued sequence spaces; Orlicz function; AK-space; duality; barrelled space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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