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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 a characterization of Pettis integrable multifunctions

Ziat H.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 3

227-230

We present a rectification of the proof of the implication i) -> ii) in Theorem 3.2 of [4]. This result gives a charactrization of Pettis integrable multifunctions with convex weakly compact values.

The Mackey topolgy for locally convex modules over a valuation ring

Kubzdela A.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 1

27-36

In this paper we study the duality for locally convex modules over the unit disk of a spherically complete valued field. We consider a dual pair for arbitrary locally convex B[K]-modules and pairs consisting of a locally convex module and its dual. We prove that the Mackey topology for an arbitrary locally convex B[K]-module exists. This extends some results of Van Tiel [1] obtained for locally convex spaces. Some additional facts for compatible topologies on c-compact B[K]-modules are included.