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w*-Basic Sequences and Reflexivity of Banach Spaces

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Abstract

We observe that a separable Banach space X is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if ℒ(X, Y) is not reflexive for reflexive X and Y then ℒ(X 1, Y) is is not reflexive for some X 1 ⊂ X, X 1 having a basis.

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Authors and Affiliations

  1. Mathematical Institute, Academy of Sciences of the Czech Republic, Zitna 25, CZ-115 67, Praha 1, Czech Republic

    Kamil John

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  1. Kamil John
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Additional information

This work was supported by the grants No. 201/03/0041 and No. 201/04/0090 of the Grant Agency of the Czech Republic and by the grant No. A1019801 of the Academy of Sciences of the Czech Republic.

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John, K. w*-Basic Sequences and Reflexivity of Banach Spaces. Czech Math J 55, 677–681 (2005). https://doi.org/10.1007/s10587-005-0054-5

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  • DOI: https://doi.org/10.1007/s10587-005-0054-5

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