Abstract: We study weakly precompact sets and operators. We show that an operator is weakly precompact if and only if its adjoint is pseudo weakly compact. We study Banach spaces with the p-L-limited^* and the p-(SR^*) properties and characterize these classes of Banach spaces in terms of p-L-limited^* and p-Right^* subsets. The p-L-limited^* property is studied in some spaces of operators.
Keywords: p-Right^* set; Right^* set; DP p-convergent operator; weakly precompact operator; limited p-convergent operator
DOI: DOI 10.14712/1213-7243.2024.013
AMS Subject Classification: 46B20 46B25 46B28