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

摘要

The p -Gelfand–Phillips property (1 $${leq}$$ ≤ p < ∞) 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 $${ightarrow}$$ → Y is weakly compact, for every Banach space Y .