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Keywords:
Dunford-Pettis property of order $p$; $p$-convergent operator; complemented spaces of operators
Summary:
Equivalent formulations of the Dunford-Pettis property of order $p$ (${DPP}_p$), $1<p<\infty$, 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 $L(X,Y)$.
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