Some approximation results in Musielak-Orlicz spaces

Ahmed Youssfi; Youssef Ahmida

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 2, page 453-471
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Youssfi, Ahmed, and Ahmida, Youssef. "Some approximation results in Musielak-Orlicz spaces." Czechoslovak Mathematical Journal 70.2 (2020): 453-471. <http://eudml.org/doc/297057>.

@article{Youssfi2020,
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.},
author = {Youssfi, Ahmed, Ahmida, Youssef},
journal = {Czechoslovak Mathematical Journal},
keywords = {approximate identity; Musielak-Orlicz space; density of smooth functions},
language = {eng},
number = {2},
pages = {453-471},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some approximation results in Musielak-Orlicz spaces},
url = {http://eudml.org/doc/297057},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Youssfi, Ahmed
AU - Ahmida, Youssef
TI - Some approximation results in Musielak-Orlicz spaces
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 2
SP - 453
EP - 471
AB - 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.
LA - eng
KW - approximate identity; Musielak-Orlicz space; density of smooth functions
UR - http://eudml.org/doc/297057
ER -

References

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