  In the present paper we study unconditionally $p$-converging operators and
Dunford-Pettis property of order $p$. New characterizations of unconditionally
$p$-converging operators and Dunford-Pettis property of order $p$ are
established. Six quantities are defined to measure how far an operator is from
being unconditionally $p$-converging. We prove quantitative versions of
relationships of completely continuous operators,unconditionally $p$-converging
operators and unconditionally converging operators. We further investigate
possible quantifications of the Dunford-Pettis property of order $p$.
