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The p-Gelfand-Phillips property (1 p < a) is studied in spaces of operators. Dunford-Pettis type like sets are studied in Banach spaces. We discuss Banach spaces X with the property that every p-convergent operator T: X Y is weakly compact, for every Banach space Y.

The p-Gelfand–Phillips property in spaces of operators and Dunford–Pettis like sets