Strict convexity of Orlicz spaces under renorming

Abstract

Let Φ be an Orlicz function and $L^{\Phi }(X,\Sigma ,\mu )$ be the corresponding Orlicz space on a non-atomic, σ-finite, complete measure space $(X,\Sigma ,\mu )$. It is known that strict convexity of the whole spaces are the most essential and important geometric notion in the geometric theory of Banach spaces. So, we describe the strict convexity of Orlicz spaces equipped with the s-norm and some of its consequences. On the other hand, it is known that the geometric properties of Orlicz space depends on the norm. Thus, our study generalizes and unifies the results that have been obtained for the Orlicz norm, the Luxemburg norm and the p-Amemiya norm separately.