Continuity of homomorphisms on complete metrizable topological algebras | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 158، دوره 13، شماره 2، مهر 2022، صفحه 1983-1987 اصل مقاله (332.95 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.22136.2335 | ||
| نویسندگان | ||
| Ganesa Moorthy C؛ Siva G* | ||
| Department of Mathematics, Alagappa University, Karaikudi-630 003, India | ||
| چکیده | ||
| Let $A$ be an $F$-algebra over the complex field. Let $B$ be an $F$-algebra such that the intersection of kernels of all continuous multiplicative linear functionals on $B$ is singleton zero. If any nonempty open subset of the collection $M(B)$ of all continuous multiplicative linear functionals in the Gelfand topology contains uncountably many functionals or if $B$ is a commutative Frechet algebra such that $M(B)$ has no isolated points, then any homomorphism from $A$ onto a dense finitely generated subalgebra of $B$ is continuous. This result has been proved in this article which is similar to a result derived by R.L. Carpenter. | ||
| کلیدواژهها | ||
| Homomorphism؛ Closed graph theorem؛ Frechet algebra | ||
| مراجع | ||
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