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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 | ||
| تاریخ دریافت: 28 آذر 1399، تاریخ بازنگری: 18 اسفند 1399، تاریخ پذیرش: 07 خرداد 1400 | ||
| 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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[1] M. E. Azhari, Functional continuity of unital B0-algebras with orthogonal bases, Le Matematiche 72 (2017), 97–102. [2] R. L. Carpenter, Uniqueness of topology for commutative semisimple F-algebras, Proc. Amer. Math. Soc. 29 (1971), 113–117. [3] S.M. Corson and I. Kazachkov, On preservation of automatic continuity, Arxiv: 1901.0901.09279v1 [math.GR], (2019), 1-14.[4] P.A. Dabhi and H.V. Dedania, On the uniqueness of uniform norms and C ∗ -norms, Studia Math. 191 (2009), 263–270. [5] A.P. Farajzadeh and M.R. Omidi, Almost multiplicative maps and ε-spectrum of an element in Fr´echet Q-algebra, Filomat 33 (2019), 1445–1452. [6] M. Eshaghi Gordji, A. Jabbari and E. Karapinar, Automatic continuity of n-homomorphisms between Banach algebras, Bull. Iran. Math. Soc. 41 (2015), 1207–1211. [7] T. G. Honary, Automatic continuity of homomorphisms between Banach algebras and Frechet algebras, Bull. Iranian Math. Soc., 32 (2006), 1-11. [8] T.G. Honary, M. Omidi and A.H. Sanatpour, Automatic continuity of almost multiplicative linear functionals on Fr´echet algebras, Bull. Korean Math. Soc. 53 (2016), 641–649. [9] E. A. Michael, Locally multiplicatively convex topological algebras, Mem. Amer. Math. Soc., 11 (1952). [10] C.G. Moorthy and G. Siva, Automatic continuity of Jordan almost multiplicative maps on special Jordan Banach algebras, Eur. J. Math. Appl. 2 (2022), 1–6. [11] M.R. Omidi, A.P. Farajzadeh, E. Soori and B.O. Gillan, Automatic continuity on fundamental locally multiplicative topological algebras, Thai J. Math. 17 (2019), 155–164. [12] I. Pastukhova, Automatic continuity of homomorphisms between topological inverse semigroups, Topol. Algebra Appl. 6 (2019), 60–66. [13] S.R. Patel, Uniqueness of the Frechet algebra topology on certain Frechet algebras, Studia Math. 234 (2016), 31–47. [14] M. Rosenfeld, Commutative F-algebras, Pacific J. Math. 16 (1966), 159–166. [15] G. Siva and C.G. Moorthy, Uniqueness of F-algebra topology for commutative semisimple algebras, Bull. Iran. Math. Soc. 45 (2019), 1871–1877. [16] G. Siva and C.G. Moorthy, Functional continuity of topological algebras with orthonormal bases, Asian-Eur. J. Math. 14 (2020), 1–15. [17] R. Skillicorn, The uniqueness-of-norm problem for Calkin algebras, Math. Proc. of Royal Irish Acad. 2 (2015), 1–8. [18] A. R. Villena, Uniqueness of the topology on spaces of vector-valued functions, J. London Math. Soc. 64 (2001), 445–456. [19] A. Zivari-Kazempour, Automatic continuity of n-Jordan homomorphisms on Banach algebras, Commun. Korean Math. Soc. 33 (2018), 165–170. | ||
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