Omidi, M. R.; Oulfatian, B.; Zivari-Kazempour, A. Almost Jordan homomorphisms on Fréchet algebras. (English) Zbl 1462.46059 Quaest. Math. 43, No. 10, 1467-1476 (2020). The following result is proved: Let \(A\) be a commutative Fréchet algebra and let \(T \colon A \rightarrow \mathbb{C}\) be an almost Jordan homomorphism. If \(T\) is not continuous then \(T\) is a homomorphism. Some automatic continuity results about maps on commutatitve Fréchet \(Q\)-algebras are also shown. Reviewer: Jerónimo Alaminos Prats (Granada) Cited in 3 Documents MSC: 46H40 Automatic continuity 47B48 Linear operators on Banach algebras 46J05 General theory of commutative topological algebras Keywords:almost Jordan homomorphism; almost multiplicative maps; Fréchet algebras; \(Q\)-algebras; automatic continuity PDFBibTeX XMLCite \textit{M. R. Omidi} et al., Quaest. Math. 43, No. 10, 1467--1476 (2020; Zbl 1462.46059) Full Text: DOI References: [1] Baker, J., The stability of cosine equation, Proc. Amer. Math. Soc, 80, 3, 411-416 (1980) · Zbl 0448.39003 · doi:10.1090/S0002-9939-1980-0580995-3 [2] Dales, H. G., Banach Algebras and Automatic Continuity (2000), London Mathematical Society, Monograph 24, Clarendon Press: London Mathematical Society, Monograph 24, Clarendon Press, Oxford · Zbl 0981.46043 [3] Eshaghi Gordji, M.; Jabbari, A.; Karapinar, AND E., Automatic continuity of surjective n-homomorphisms on Banach algebras, Bull. Iranian Math. Soc, 41, 5, 1207-1211 (2015) · Zbl 1373.46040 [4] Fragoulopoulou, M., ,, Topological Algebras with Involution (2005), North-Holland Math. Studies: North-Holland Math. Studies, Amsterdam · Zbl 1197.46001 [5] Goldmann, H., Uniform Fréchet Algebras (1990), North Holland: North Holland, Amsterdam · Zbl 0718.46017 [6] Hejazian, Sh.; Mirzavaziri, M.; Moslehian, M. S., n-homomorphisms, Bull. Iranian Math. Soc., 31, 1, 13-23 (2005) · Zbl 1121.47028 [7] Honary, T. G., Automatic continuity of homomorphisms between Banach algebras and Fréchet algebras, Bull. Iranian Math. Soc, 32, 1-11 (2006) · Zbl 1140.46023 [8] Husain, T., Multiplicative Functionals on Topological Algebras (1983), Pitman Books Limited: Pitman Books Limited, Boston/London/Melbourne · Zbl 0514.46030 [9] Jarosz, K., Perturbations of Banach Algebras (1985), Lecture Notes in Mathematics, Springer-Verlag: Lecture Notes in Mathematics, Springer-Verlag, Berlin · Zbl 0557.46029 [10] Mallios, A., Topological Algebras (1986), North Holland: North Holland, Amsterdam · Zbl 0597.46046 [11] Michael, E. A., Locally multiplicatively convex topological algebras, Mem. Amer. Math. Soc, 11, 1-82 (1952) · Zbl 0047.35502 [12] Zelazko, W., A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math, 30, 83-85 (1968) · Zbl 0162.18504 · doi:10.4064/sm-30-1-83-85 [13] Zivari-Kazempour, A., A characterization of 3-Jordan homomorphism on Banach algebras, Bull. Aust. Math. Soc, 93, 2, 301-306 (2016) · Zbl 1334.47037 · doi:10.1017/S0004972715001057 [14] Zivari-Kazempour, A., Automatic continuity of n-Jordan homomorphisms on Banach algebras, Comm/un. Korean Math. Soc, 33, 1, 165-170 (2018) · Zbl 1473.46053 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.