Unconditionally $p$-converging operators and Dunford-Pettis Property of   order $p$
  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 $p$. 
Dongyang Chen, J. Alejandro Ch\'avez-Dom\'inguez, Lei Li
math.FA