Czechoslovak Mathematical Journal, first online, pp. 1-19


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
Classification MSC:  46E30, 46B10
DOI:  10.21136/CMJ.2019.0355-18

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Affiliations:   Ahmed Youssfi, Youssef Ahmida, Sidi Mohamed Ben Abdellah University, National School of Applied Sciences, Laboratory of Engineering, Systems and Applications (LISA), My Abdellah Avenue, Road Imouzer, P.O. Box 72 Fès-Principale, 30 000 Fez, Morocco, e-mail: ahmed.youssfi@gmail.com, ahmed.youssfi@usmba.ac.ma, youssef.ahmida@usmba.ac.ma


 
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