Advanced Search

A criterion for strongly exposed points of the unit ball $B\left(l_M\right)$ in Musielak-Orlicz sequence spaces $l_M$ equipped with Orlicz norm is given.

Let X,Y be Banach spaces, f: X → Y be an isometry with f(0) = 0, and $T:\overline{span}\left(f\left(X\right)\right)\to X$ be the Figiel operator with $T\circ f=I{d}_X$ and ||T|| = 1. We present a sufficient and necessary condition for the Figiel operator T to admit a linear isometric right inverse. We also prove that such a right inverse exists when $\overline{span}\left(f\left(X\right)\right)$ is weakly nearly strictly convex.