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- Title
GLEASON-KAHANE-ZELAZKO THEOREM IN JORDAN BANACH ALGEBRAS.
- Authors
MAOUCHE, ABDELAZIZ
- Abstract
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.
- Subjects
BANACH algebras; JORDAN algebras; NONASSOCIATIVE algebras; ASSOCIATIVE algebras; FUNCTIONALS
- Publication
Gulf Journal of Mathematics, 2024, Vol 16, Issue 2, p39
- ISSN
2309-4966
- Publication type
Article
- DOI
10.56947/gjom.v16i2.1868