Diameter of weak neighborhoods and the Radon-Nikodym property in Orlicz-Lorentz spaces
A Kamińska, HJ Tag�- arXiv preprint arXiv:1606.00909, 2016 - arxiv.org
A Kamińska, HJ Tag
arXiv preprint arXiv:1606.00909, 2016•arxiv.orgGiven an Orlicz $ N $-function $\varphi $ and a positive decreasing weight $ w $, we present
criteria of the diameter two property and of the Radon-Nikod\'ym property in Orlicz-Lorentz
function and sequence spaces $\Lambda_ {\varphi, w} $ and $\lambda_ {\varphi, w} $. We
show that in the spaces $\Lambda_ {\varphi, w} $ or $\lambda_ {\varphi, w} $ equipped with
the Luxemburg norm, the diameter of any relatively weakly subset of the unit ball in these
spaces is two if and only if $\varphi $ does not satisfy the appropriate $\Delta_2 $ condition�…
criteria of the diameter two property and of the Radon-Nikod\'ym property in Orlicz-Lorentz
function and sequence spaces $\Lambda_ {\varphi, w} $ and $\lambda_ {\varphi, w} $. We
show that in the spaces $\Lambda_ {\varphi, w} $ or $\lambda_ {\varphi, w} $ equipped with
the Luxemburg norm, the diameter of any relatively weakly subset of the unit ball in these
spaces is two if and only if $\varphi $ does not satisfy the appropriate $\Delta_2 $ condition�…
Given an Orlicz -function and a positive decreasing weight , we present criteria of the diameter two property and of the Radon-Nikod\'ym property in Orlicz-Lorentz function and sequence spaces and . We show that in the spaces or equipped with the Luxemburg norm, the diameter of any relatively weakly subset of the unit ball in these spaces is two if and only if does not satisfy the appropriate condition, while they have the Radon-Nikod\'ym property if and only if satisfies the appropriate condition.
arxiv.org