Czechoslovak Mathematical Journal, Vol. 70, No. 2, pp. 453-471, 2020
Some approximation results in Musielak-Orlicz spaces
Ahmed Youssfi, Youssef Ahmida
Received July 30, 2018. Published online December 17, 2019.
Abstract: We prove the continuity in norm of the translation operator in the Musielak-Orlicz $L_M$ spaces. An application to the convergence in norm of approximate identities is given, whereby we prove density results of the smooth functions in $L_M$, in both the modular and norm topologies. These density results are then applied to obtain basic topological properties.
Keywords: approximate identity; Musielak-Orlicz space; density of smooth functions