Linear topological properties of the Lumer-Smirnov class of the polydisc

Marek Nawrocki

ArticleOriginal scientific text

Title

Linear topological properties of the Lumer-Smirnov class of the polydisc

Authors ¹

Affiliations

Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland

Abstract

Linear topological properties of the Lumer-Smirnov class

L N_{*} (U^{n})

of the unit polydisc

U^{n}

are studied. The topological dual and the Fréchet envelope are described. It is proved that

L N_{*} (U^{n})

has a weak basis but it is nonseparable in its original topology. Moreover, it is shown that the Orlicz-Pettis theorem fails for

L N_{*} (U^{n})

.

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Title

Linear topological properties of the Lumer-Smirnov class of the polydisc

Affiliations

Abstract

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