Advanced Search

Linear topological properties of the Lumer-Smirnov class $L{N}_{\ast }{(}^n)$ of the unit polydisc ${}^n$ are studied. The topological dual and the Fréchet envelope are described. It is proved that $L{N}_{\ast }{(}^n)$ has a weak basis but it is nonseparable in its original topology. Moreover, it is shown that the Orlicz-Pettis theorem fails for $L{N}_{\ast }{(}^n)$.