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A note on some complemented spaces of operators

Volume 150 / 2017

Ioana Ghenciu Colloquium Mathematicum 150 (2017), 207-215 MSC: Primary 46B20, 46B25, 46B28; Secondary 47L20. DOI: 10.4064/cm6977-11-2016 Published online: 24 July 2017

Abstract

Let $W(X,Y)$, $\mathit {Pwc}(X,Y)$, $\mathit {CC}(X,Y)$, and $\mathit {UC}(X,Y)$ denote respectively the sets of all weakly compact, pseudo weakly compact, completely continuous, and unconditionally converging operators from $X$ to $Y$. We use classical results of Kalton to study the complementability of the space $W(X,Y)$ in the spaces $\mathit {Pwc}(X,Y)$, $\mathit {UC}(X,Y)$, and $\mathit {CC}(X,Y)$.

Authors

  • Ioana GhenciuMathematics Department
    University of Wisconsin-River Falls
    410 S. 3rd Street
    River Falls, WI 54022-500, U.S.A.
    e-mail

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