TY - JOUR
T1 - GLEASON-KAHANE-ZELAZKO THEOREM IN JORDAN BANACH ALGEBRAS
AU - Maouche, Abdelaziz
N1 - Publisher Copyright:
© 2024, Canadian University of Dubai. All rights reserved.
PY - 2024/4/12
Y1 - 2024/4/12
N2 - 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.
AB - 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.
KW - (almost) multiplicative linear functional
KW - condition spectrum
KW - Jordan Banach algebra
KW - spectrum
UR - http://www.scopus.com/inward/record.url?scp=85191871028&partnerID=8YFLogxK
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UR - https://www.mendeley.com/catalogue/714cb3f2-5ebf-3a83-ad26-2d2b279a209e/
U2 - 10.56947/gjom.v16i2.1868
DO - 10.56947/gjom.v16i2.1868
M3 - Article
AN - SCOPUS:85191871028
SN - 2309-4966
VL - 16
SP - 39
EP - 51
JO - Gulf Journal of Mathematics
JF - Gulf Journal of Mathematics
IS - 2
ER -