Zivari-Kazempour, A. When is a bi-Jordan homomorphism bi-homomorphism? (English) Zbl 1483.47073 Kragujevac J. Math. 42, No. 4, 485-493 (2018). Summary: For Banach algebras \(\mathcal{A}\) and \(\mathcal{B}\), we show that, if \(\mathcal{U}=\mathcal{A}\times\mathcal{B}\) is commutative (weakly commutative), then each bi-Jordan homomorphism from \(\mathcal{U}\) into a semisimple commutative Banach algebra \(\mathcal{D}\) is a bi-homomorphism. We also prove the same result for 3-bi-Jordan homomorphism with the additional hypothesis that the Banach algebra \(\mathcal{U}\) is unital. Cited in 2 Documents MSC: 47B48 Linear operators on Banach algebras 46L05 General theory of \(C^*\)-algebras 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) Keywords:n-bi-homomorphism; n-bi-Jordan homomorphism; weakly commutative PDFBibTeX XMLCite \textit{A. Zivari-Kazempour}, Kragujevac J. Math. 42, No. 4, 485--493 (2018; Zbl 1483.47073) Full Text: Link References: [1] J. Bračič and M. S. Moslehian,On automatic continuity of 3-homomorphisms on Banach algebras, Bull. Malays. Math. Sci. Soc.30(2) (2007), 195-200. · Zbl 1153.46031 [2] M. Eshaghi Gordji,n-Jordan homomorphisms, Bull. Aust. Math. Soc.80(1) (2009), 159-164. · Zbl 1177.47046 [3] M. Eshaghi Gordji, T. Karimi and S. Kaboli Gharetapeh,Approximately n-Jordan homomorphisms on Banach algebras, J. Inequal. Appl.2009(2009), 1-8. · Zbl 1162.39017 [4] E. Gselmann,On approximate n-Jordan homomorphisms, Ann. Math. Sil.28(2014), 47-58. · Zbl 1369.46038 [5] Sh. Hejazian, M. Mirzavaziri and M. S. Moslehian,n-homomorphisms, Bull. Iranian Math. Soc. 31(1) (2005), 13-23. · Zbl 1121.47028 [6] I. N. Herstein,Jordan homomorphisms, Trans. Amer. Math. Soc.81(1956), 331-341. · Zbl 0073.02202 [7] Y. H. Lee,Stability of n-Jordan homomorphisms from a normed algebra to a Banach algebra, Abstr. Appl. Anal.2013(2013), 1-5. · Zbl 1470.39054 [8] T. Miura, S.-E. Takahasi and G. Hirasawa,Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras, J. Inequal. Appl.2005(2005), 435-441. · Zbl 1104.39026 [9] W. Zelazko,A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math.30(1968), 83-85. · Zbl 0162.18504 [10] A. Zivari-Kazempour,A characterization of Jordan homomorphism on Banach algebras, Chinese J. Math.2014(2014), 1-3. · Zbl 1315.46052 [11] A. Zivari-Kazempour,A characterization of 3-Jordan homomorphisms on Banach algebras, Bull. Aust. Math. Soc.93(2) (2016), 301-306. · Zbl 1334.47037 [12] A. Zivari-Kazempour,A characterization of Jordan and 5-Jordan homomorphisms between Banach algebras, Asian-Eur. J. Math. (2017) DOI 10.1142/S1793557118500213. · Zbl 1377.46033 [13] A. Zivari-Kazempour,A characterization of bi-Jordan homomorphisms on Banach algebras, Int. J. Anal.2017(2017), 1-5 · Zbl 1377.46033 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.