On the properties $(\mathbf{wL})$ and $(\mathbf{wV})$

Rok, strany: 2016, 1399 - 1412

We characterize Banach spaces $X$ with spaces with property $(wL)$, i.e., spaces with the property that every $L$-subset of $X^*$ is weakly precompact. We prove that a Banach space $X$ has property $(wL)$ if and only if for any Banach space $Y$, any completely continuous operator $T: X\to Y$ has weakly precompact adjoint if and only if any completely continuous operator $T: X\to \ell_∞$ has weakly precompact adjoint. We prove that if $E$ is a Banach space and $F$ is a reflexive subspace of $E^*$ such that $^\perpF$ has property $(wL)$, then $E$ has property $(wL)$. We show that a space $E$ has property $RDP^*$ (resp. the $DPrcP$) if and only if any closed separable subspace of $E$ has property $RDP^*$ (resp. the $DPrcP$). We also show that $G$ has property $(wL)$ if under some conditions $K_w^*(E^*,F)$ contains the dual of $G$.

ISO 690:

Ghenciu, I. 2016. On the properties $(\mathbf{wL})$ and $(\mathbf{wV})$. In Mathematica Slovaca, vol. 66, no.6, pp. 1399-1412. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0232

APA:

Ghenciu, I. (2016). On the properties $(\mathbf{wL})$ and $(\mathbf{wV})$. Mathematica Slovaca, 66(6), 1399-1412. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0232