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

Marek Nawrocki (1992)

Studia Mathematica

Linear topological properties of the Lumer-Smirnov class L N ( n ) of the unit polydisc n are studied. The topological dual and the Fréchet envelope are described. It is proved that L N ( 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 ( n ) .

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