A characterization of singular endomorphisms of a barrelled Pták space

[摘要] The concept of topological divisor of zero has been extended to endomorphismsof 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.

[学科分类] 数学（综合）