Geometry of Banach spaces having shrinking approximations of the identity
Geometry of Banach spaces having shrinking approximations of the identity
Let $a,c\geq 0$ and let $B$ be a compact set of scalars. We introduce property $M^{\ast }(a,B,c)$ of Banach spaces $X$ by the requirement that \begin{equation*}\limsup _{\nu }\| ax_{\nu }^{\ast } +bx^{\ast }+cy^{\ast }\|\leq \limsup _{\nu }\| x_{\nu }^{\ast }\|\quad \forall b\in B \end{equation*} whenever $(x_{\nu }^{\ast })$ is a …