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Keywords:
$p$-Right$^*$ set; Right$^*$ set; DP $p$-convergent operator; weakly precompact operator; limited $p$-convergent operator
Summary:
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.
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