We review the celebrated Gleason-Kahane-Zelazko and Kowalski-Slodkowski theorems from the setting of associative Banach algebras to the wider class of nonassociative Jordan Banach algebras. We introduce the notion of almost multiplicative linear functionals in Jordan Banach algebras and prove a theorem extending a former result of B.E. Johnson for Banach algebras by employing the more recent concept of condition spectrum. We show how to rediscover the Gleason-Kahane-Zelazko theorem for Jordan Banach algebras from the corresponding version for almost multiplicative linear functionals.
CITATION STYLE
Maouche, A. (2024). GLEASON-KAHANE-ZELAZKO THEOREM IN JORDAN BANACH ALGEBRAS. Gulf Journal of Mathematics, 16(2), 39–51. https://doi.org/10.56947/gjom.v16i2.1868
Mendeley helps you to discover research relevant for your work.