Geodesic
Local structure of generalized Orlicz−Lorentz function spaces
Commentationes Mathematicae, Tome 55 (2015) no. 2, p. 211−227.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

We study the local structure of a separated point \(x\) in the generalized Orlicz-Lorentz space \(\Lambda ^{\varphi }\) which is a symmetrization of the respective Musielak-Orlicz space \(L^{\varphi }\). We present criteria for an \(LM\) point and a \(\mathit{UM}\) point, and sufficient conditions for a point of order continuity and an \(\mathit{LLUM}\) point, in the space \(\Lambda ^{\varphi }\). We prove also a characterization of strict monotonicity of the space \(\Lambda ^{\varphi }\).
DOI : 10.14708/cm.v55i2.1121
Classification : 46E30, 46B20, 46B42
Mots-clés : symmetric spaces, symmetrization of the Banach function space, generalized Orlicz-Lorentz space, Musielak-Orlicz space, monotonicity properties, order continuity, local structure of a separated point 
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Paweł Kolwicz. Local structure of generalized Orlicz−Lorentz function spaces. Commentationes Mathematicae, Tome 55 (2015) no. 2, p.  211−227. doi : 10.14708/cm.v55i2.1121. http://geodesic.mathdoc.fr/articles/10.14708/cm.v55i2.1121/

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