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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.
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Tom
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1--10
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bibliogr. 7 poz.
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- Instituto de Mathematicas, Universidad Nacional Autonoma de Mexico Circuito Exterior, Ciudad Universitaria, 04510 Mexico, D.F., hugo@matem.unam.mx
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bwmeta1.element.baztech-article-BUS1-0006-0085