Nawrocki, Marek Linear topological properties of the Lumer-Smirnov class of the polydisc. (English) Zbl 0814.46018 Stud. Math. 102, No. 1, 87-102 (1992). Summary: Linear topological properties of the Lumer-Smirnov class \(LN_ *(\mathbb{U}^ n)\) of the unit polydisc \(\mathbb{U}^ n\) are studied. The topological dual and the Fréchet envelope are described. It is proved that \(LN_ *(\mathbb{U}^ n)\) has a weak basis but it is nonseparable in its original topology. Moreover, it is shown that the Orlicz-Pettis theorem fails for \(LN_ *(\mathbb{U}^ n)\). MSC: 46E10 Topological linear spaces of continuous, differentiable or analytic functions 46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces 46B22 Radon-Nikodým, Kreĭn-Milman and related properties 32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables 46E25 Rings and algebras of continuous, differentiable or analytic functions Keywords:linear topological properties of the Lumer-Smirnov class; topological dual; Fréchet envelope; weak basis; Orlicz-Pettis theorem PDFBibTeX XMLCite \textit{M. Nawrocki}, Stud. Math. 102, No. 1, 87--102 (1992; Zbl 0814.46018) Full Text: DOI EuDML