On totally smooth subspaces of Banach spaces: the Vlasov theorem revisited
Volume 238 / 2017
Studia Mathematica 238 (2017), 91-99
MSC: Primary 46B20; Secondary 46A22, 46B04.
DOI: 10.4064/sm8623-12-2016
Published online: 24 February 2017
Abstract
Let $X$ be a Banach space and let $Y$ be a closed subspace of $X$. We establish new geometric characterizations for $Y$ to be totally smooth in $X$, meaning that every closed subspace of $Y$ has Phelps’ property $U$ in $X$. In particular, this gives a new self-contained proof for a recent theorem of Liao and Wong, and an improved proof for a theorem of Vlasov.
