Geodesic
Some approximation results in Musielak-Orlicz spaces
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 453-471.

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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.
DOI : 10.21136/CMJ.2019.0355-18
Classification : 46B10, 46E30
Keywords: approximate identity; Musielak-Orlicz space; density of smooth functions 
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Youssfi, Ahmed; Ahmida, Youssef. Some approximation results in Musielak-Orlicz spaces. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 453-471. doi : 10.21136/CMJ.2019.0355-18. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0355-18/

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