Geodesic
A note on Dunford-Pettis like properties and complemented spaces of operators
Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 2, pp. 207-222.

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Equivalent formulations of the Dunford-Pettis property of order $p$ (${DPP}_p$), $1$, are studied. Let $L(X,Y)$, $W(X,Y)$, $K(X,Y)$, $U(X,Y)$, and $C_p(X,Y)$ denote respectively the sets of all bounded linear, weakly compact, compact, unconditionally converging, and $p$-convergent operators from $X$ to $Y$. Classical results of Kalton are used to study the complementability of the spaces $W(X,Y)$ and $K(X,Y)$ in the space $C_p(X,Y)$, and of $C_p(X,Y)$ in $U(X,Y)$ and $L(X,Y)$.
DOI : 10.14712/1213-7243.2015.238
Classification : 46B20, 46B25, 46B28
Keywords: Dunford-Pettis property of order $p$; $p$-convergent operator; complemented spaces of operators 
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Ghenciu, Ioana. A note on Dunford-Pettis like properties and complemented spaces of operators. Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 2, pp. 207-222. doi : 10.14712/1213-7243.2015.238. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.238/

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