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1 results

  • On Spaces of Compact Operators in Non-Archimedean Banach Spaces

  • Takemitsu Kiyosawa
  • Journal:
    Canadian Mathematical Bulletin / Volume 32 / Issue 4 / 01 December 1989
    Published online by Cambridge University Press:
    20 November 2018, pp. 450-458
    Print publication:
    01 December 1989
    • Article
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  • Let K be a non-trivial complete non-Archimedean valued field and let E be an infinite-dimensional Banach space over K. Some of the main results are:

    (1) K is spherically complete if and only if every weakly convergent sequence in l∞ is norm-convergent.

    (2) If the valuation of K is dense, then C0 is complemented in E if and only if C(E,c0) is n o t complemented in L(E,c0), where L(E,c0) is the space of all continuous linear operators from E to c0 and C(E,c0) is the subspace of L(E, c0) consisting of all compact linear operators.