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C. Ganesa Moorthy, G. Siva, Automatic continuity of Jordan almost multiplicative maps on special Jordan Banach algebras, Eur. J. Math. Appl. 2 (2022), Article ID 9.

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Volume 2 (2022), Article ID 9

https://doi.org/10.28919/ejma.2022.2.9

Published: 02/05/2022

Abstract:

If $T: \Lambda \rightarrow \Gamma$ is a dense range homomorphism from a Banach algebra $\Lambda$ to a semisimple Banach algebra $\Gamma$, then the automatic continuity of $T$ is being a long-standing open question. The concept of Jordan almost multiplicative maps between Jordan Banach algebras is introduced, and an extension of this open question to Jordan Banach algebras is considered. Also, a partial answer to the extended open question is derived in the sense that every dense range Jordan almost multiplicative map $T$ from a special Jordan Banach algebra $\Lambda^{+}$ to a semisimple special Jordan Banach algebra $\Gamma^{+}$, with an additional condition on $\Lambda^{+}$ and $\Gamma^{+}$, is continuous.

How to Cite:

C. Ganesa Moorthy, G. Siva, Automatic continuity of Jordan almost multiplicative maps on special Jordan Banach algebras, Eur. J. Math. Appl. 2 (2022), Article ID 9. https://doi.org/10.28919/ejma.2022.2.9