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Barrelled Weakly Köthe–Orlicz Summable Sequence Spaces

Author

Listed:
  • 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)

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.

Suggested Citation

  • Issam Aboutaib & Janusz Brzdęk & Lahbib Oubbi, 2023. "Barrelled Weakly Köthe–Orlicz Summable Sequence Spaces," Mathematics, MDPI, vol. 12(1), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:88-:d:1308028
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