TY - JOUR
T1 - On the Bicomplex Gleason–Kahane–Żelazko Theorem
AU - Luna-Elizarrarás, M. E.
AU - Pérez-Regalado, C. O.
AU - Shapiro, M.
N1 - Publisher Copyright:
© 2015, Springer Basel.
PY - 2016/2/1
Y1 - 2016/2/1
N2 - We prove that a bicomplex linear functional acting on a bicomplex Banach algebra (with a hyperbolic-valued norm) in such a way that invertible elements are transformed into invertible bicomplex numbers is, in fact, a multiplicative functional and thus, an algebra homomorphism. We give two proofs of this. The first of them is based on the theory of bicomplex holomorphic functions and we present here a number of previously not published facts; the second uses its complex antecedent (classic Gleason–Kahane–Żelazko theorem).
AB - We prove that a bicomplex linear functional acting on a bicomplex Banach algebra (with a hyperbolic-valued norm) in such a way that invertible elements are transformed into invertible bicomplex numbers is, in fact, a multiplicative functional and thus, an algebra homomorphism. We give two proofs of this. The first of them is based on the theory of bicomplex holomorphic functions and we present here a number of previously not published facts; the second uses its complex antecedent (classic Gleason–Kahane–Żelazko theorem).
KW - Bicomplex functionals
KW - Bicomplex holomorphic functions
KW - Bicomplex modules
KW - Gleason–Kahane–Żelazko theorem
KW - Hyperbolic-valued norm
UR - http://www.scopus.com/inward/record.url?scp=84955739031&partnerID=8YFLogxK
U2 - 10.1007/s11785-015-0455-x
DO - 10.1007/s11785-015-0455-x
M3 - Artículo
SN - 1661-8254
VL - 10
SP - 327
EP - 352
JO - Complex Analysis and Operator Theory
JF - Complex Analysis and Operator Theory
IS - 2
ER -