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Strictly and uniformly monotone Musielak-Orlicz spaces and applications to best approximation. (English) Zbl 0749.41031

Author’s abstract: several monotonicity properties of the Luxemburg norm in Musielak-Orlicz spaces \(L_ \varphi(\mu)\) and \(E_ \varphi(\mu)\) over nonatomic measure spaces are characterized in terms of the function \(\varphi\). For \(L_ \varphi(\mu)\) it is proved that all these properties coincide with the absolute continuity of the norm and \(\varphi>0\). Some applications to best approximation are given, even for general Banach lattices.

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A50 Best approximation, Chebyshev systems
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