International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 3, Pages 529-536
doi:10.1155/S0161171282000490
A characterization of singular endomorphisms of a barrelled Pták space
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Received 29 October 1980; Revised 2 July 1981
Copyright © 1982 Damir Franekić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The concept of topological divisor of zero has been extended to endomorphisms
of a locally convex topological vector space (LCTVS). A characterization of singular endomorphisms, similar to that of Yood [1], is obtained for endomorphisms of a barrelled Pták (fully complete) space and it is shown that each such endomorphism is a topological divisor of zero. Furthermore, properties of the adjoint of an endomorphism are characterized in terms of topological divisors of zero, and the effect of change of operator topology on such a characterization is given.