Some Rotundities of Orlicz–Lorentz Spaces

Abstract

K-UR, K-LUR and K-R are the generalizations of UR, LUR and R respectively, which are of great significance in Banach space theory. While in Orlicz–Lorentz function space \(\Lambda_{\varphi,\omega}^{\circ}[0,\gamma)\) equipped with the Orlicz norm, the research methods of K-UR, K-LUR and K-R are much more complicated than those of UR, LUR and R. In this paper we obtain some criteria of K-UR, K-LUR and K-R of \(\Lambda_{\varphi,\omega}^{\circ}[0,\gamma)\) by means of the norm of dual space and H_μ property of \(\Lambda_{\varphi,\omega}^{\circ}[0,\gamma)\).