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Banach envelopes of some quasi-Banach function spaces

Kamińska A., Kubiak D.

Commentationes Mathematicae

2016

Vol 56, No. 1

87--101

We show that under some assumptions on the Musielak−Orlicz function generating a quasi-Banach Musielak−Orlicz function space, the Banach envelope of the weighted Cesàro−Musielak−Orlicz space generated by a certain positive sublinear operator is a weighted L1-space.

On the strict convexity of Besicovitch-Musielak-Orlicz spaces of almost periodic functions equipped with the Orlicz norm

Daoui A., Morsli M., Smaali M.

Commentationes Mathematicae

2013

Vol. 53, No. 2

101--111

We characterize the strict convexity of Besicovitch-Musielak-Orlicz spaces of almost periodic functions, when it is equipped with the Orlicz norm. It is shown that this property is equivalent to the strict convexity of the Musielak-Orlicz function generating the space.

On a problem of Rolewicz concerning separable quotients of F-spaces

Wójtowicz M.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 4

313-317

Let Psi be a (nonconvex) Musielak-Orlicz function, and let (Omega, Sigma, mi) be a sigma-finite measure space. If L[psi] (mi) [is different from E[psi] (mi), where E[psi] (mi) is the space of the elements of L[psi] (mi) with absolutely continuous norm, then L[psi] (mi) has an infinite dimensional separable Banach quotient (Theorem).