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Strongly limited (Dunford–Pettis) completely continuous subspaces of operator ideals

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Abstract

By introducing the concepts of strongly limited completely continuous and strongly Dunford–Pettis completely continuous subspaces of operator ideals, it will be given some characterizations of these concepts in terms of lcc ness and DPcc ness of all their evaluation operators related to that subspace. In particular, when \(X^*\) or Y has the Gelfand–Phillips (GP) property, we give a characterization of GP property of a closed subspace \({\mathcal {M}}\) of compact operators K(X, Y) in terms of strong limited complete continuity of \({\mathcal {M}}\). Also it is shown that, each operator ideal \({\mathcal {U}}(X, Y )\) is strongly limited completely continuous, iff, \(X^*\) and Y have the GP property.

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Authors and Affiliations

  1. Department of Mathematics, Payame Noor University, Tehran, Iran

    Halimeh Ardakani

  2. Department of Mathematics, Farhangian University, Tehran, Iran

    Manijeh Salimi

  3. Department of Mathematics, Yazd University, Yazd, 89195-741, Iran

    Seyed Mohammad Moshtaghioun

Authors
  1. Halimeh Ardakani
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  2. Manijeh Salimi
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  3. Seyed Mohammad Moshtaghioun
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Correspondence to Halimeh Ardakani.

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Communicated by Tatiana Shulman.

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Ardakani, H., Salimi, M. & Moshtaghioun, S.M. Strongly limited (Dunford–Pettis) completely continuous subspaces of operator ideals. Ann. Funct. Anal. 11, 583–594 (2020). https://doi.org/10.1007/s43034-019-00039-8

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  • DOI: https://doi.org/10.1007/s43034-019-00039-8

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