Geodesic
$L$-limited-like properties on Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 4, pp. 439-457
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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.
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.
DOI : 10.14712/1213-7243.2024.013
Classification : 46B20, 46B25, 46B28
Keywords: $p$-Right$^*$ set; Right$^*$ set; DP $p$-convergent operator; weakly precompact operator; limited $p$-convergent operator 
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Ghenciu, Ioana. $L$-limited-like properties on Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 4, pp. 439-457. doi: 10.14712/1213-7243.2024.013

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