TY - JOUR
T1 - On Linear Functionals and Hahn-Banach Theorems for Hyperbolic and Bicomplex Modules
AU - Luna-Elizarrarás, M. E.
AU - Perez-Regalado, C. O.
AU - Shapiro, M.
N1 - Publisher Copyright:
© 2014, Springer Basel.
PY - 2014/11/15
Y1 - 2014/11/15
N2 - We consider modules over the commutative rings of hyperbolic and bicomplex numbers. In both cases they are endowed with norms which take values in non–negative hyperbolic numbers. The exact analogues of the classical versions of the Hahn–Banach theorem are proved together with some of their consequences. Linear functionals on these modules are studied and their relations with the corresponding hyperplanes are established. Finally, we introduce the notion of hyperbolic convexity for hyperbolic modules (in analogy with real, not complex, convexity) and establish its relation with hyperplanes.
AB - We consider modules over the commutative rings of hyperbolic and bicomplex numbers. In both cases they are endowed with norms which take values in non–negative hyperbolic numbers. The exact analogues of the classical versions of the Hahn–Banach theorem are proved together with some of their consequences. Linear functionals on these modules are studied and their relations with the corresponding hyperplanes are established. Finally, we introduce the notion of hyperbolic convexity for hyperbolic modules (in analogy with real, not complex, convexity) and establish its relation with hyperplanes.
KW - Hahn–Banach theorems
KW - Hyperbolic modules
KW - bicomplex modules
KW - hyperbolic convexity
KW - hyperbolic–valued norm
KW - hyperplanes
UR - http://www.scopus.com/inward/record.url?scp=84911461890&partnerID=8YFLogxK
U2 - 10.1007/s00006-014-0503-z
DO - 10.1007/s00006-014-0503-z
M3 - Artículo
SN - 0188-7009
VL - 24
SP - 1105
EP - 1129
JO - Advances in Applied Clifford Algebras
JF - Advances in Applied Clifford Algebras
IS - 4
ER -