Topological algebras of kernels |
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| Authors: | Athanasios Kyriazis |
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| Institution: | (1) Mathematical Institute, University of Athens, 57, Solonos Street, GR-10679 Athens, Greece |
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| Abstract: | Given a locally convex spaceE we define thelocally convex algebra of kernels
, in such a way that the set of all its proper closed 2-sided ideals coincides with the set of all closed vector subspaces of ker(h), whereh is a continuous algebra morphism of
into 
b
(E). Moreover,h is a strictly irreducible representation such that every representation :
 ;
b
(F) (F a locally convex space) is of the form = oh, where stands for a continuous isomorphis ofIm(h) into
b
(F), for a suitable topology onIm(h). |
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| Keywords: | Compatible tensorial topology algebra of kernels faithful topology Jacobson radical strictly irreducible representation |
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