7th Positivity Conference, Leiden, Netherlands, 22 - 26 July 2013, pp.25-33
The finite rank, L-and M-weakly compact operators are studied. The inclusion of these classes with one another and with the weak Dunford-Pettis, almost Dunford-Pettis and b-weakly compact operators as well as the effect of these inclusions to the order structure of spaces serving as range or domain are examined.