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1 Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1 1999

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On continuous multiplicative mappings on analytic sequence spaces

Arizmendi H.P., Carrillo A.H., Palacios L.F.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1999

[Z] 39

1-10

Let A denotes the space of all complex sequences such that an appropriate power series converges for |z|<1 and B denotes the space of all complex sequences such that an appropriate power series converges for |z|>1. In this paper we prove that A and B, provided with their normal topologies turn out to be a topo-logical (matrix) algebras. Also we show that when they are endowed with such topologies then the set of all the matrix mappings from A or B into any of these two spaces coincides with the set of all the continuous linear transformations. We also characterize all-non-zero multiplicative and continu-ous matrix mappings between those two algebras.