Ball remotal subspaces of Banach spaces
Tom 114 / 2009
Colloquium Mathematicum 114 (2009), 119-133 MSC: Primary 46B20, 47L05; Secondary 46E40. DOI: 10.4064/cm114-1-10
We study Banach spaces $X$ with subspaces $Y$ whose unit ball is densely remotal in $X$. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set $E \subseteq X$, the set of Bochner integrable functions with values in $E$ is a remotal set in $L^1(\mu , X)$.