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Spaces of diagonal operators

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Abstract.

Properties of space of diagonal operators on semi-normalized Schauder bases are studied. A necessary and sufficient condition is given for the containment of \(c_0\) in the space of compact diagonal operators on a semi-normalized Schauder basis. Using this condition it is shown that there exist semi-normalized Schauder bases of reflexive Banach spaces such that \(c_0\) does not embed in the space of compact diagonal operators on these Schauder bases.

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Authors and Affiliations

  1. 39, The Paddock, Perceton, Irvine, Ayrshire, Scotland, KA11 2AZ, UK (james.wark@btinternet.com) , , , , , , GB

    H.M. Wark

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  1. H.M. Wark
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Received January 21, 1999; in final form April 10, 2000 / Published online February 5, 2001

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Wark, H. Spaces of diagonal operators. Math Z 237, 395–420 (2001). https://doi.org/10.1007/PL00004874

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  • DOI: https://doi.org/10.1007/PL00004874

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