Complex Convexity of Orlicz–Lorentz Spaces and its Applications
Volume 52 / 2004
Bulletin Polish Acad. Sci. Math. 52 (2004), 19-38
MSC: 46E30, 46E20, 46G25.
DOI: 10.4064/ba52-1-3
Abstract
We give sufficient and necessary conditions for complex extreme points of the unit ball of Orlicz–Lorentz spaces, as well as we find criteria for the complex rotundity and uniform complex rotundity of these spaces. As an application we show that the set of norm-attaining operators is dense in the space of bounded linear operators from $d_*(w,1)$ into $d(w,1)$, where $d_*(w,1)$ is a predual of a complex Lorentz sequence space $d(w,1)$, if and only if $w\in c_0\setminus \ell _2$.
