A characterization of singular endomorphisms of a barrelled Pták space
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...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171282000490 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |