TY - JOUR
ID - 12290
TI - Strongly Zeo-product Preserving Maps on Normed Algebras Induced by a Bounded Linear Functional
JO - Khayyam Journal of Mathematics
JA - KJM
LA - en
SN -
AU - Khoddami, Ali Reza
AD - Department of Pure Mathematics, University of Shahrood, P. O. Box 3619995161-
316, Shahrood, Iran.
Y1 - 2015
PY - 2015
VL - 1
IS - 1
SP - 107
EP - 114
KW - (Jordan) zero-product preserving map
KW - strongly (Jordan) zeroproduct preserving map
KW - Arens product
KW - polynomial equation
DO - 10.22034/kjm.2015.12290
N2 - We introduce the notions of strongly zero-product (strongly Jordan zero-product) preserving maps on normed algebras. These notions are generalization of the concepts of zero-product and Jordan zero-product preserving maps. Also for a non-zero vector space V and for a non-zero linear functional f on V, we equip V with a multiplication, converting V into an associative algebra, denoted by Vf . We characterize the zero-product (Jordan zero-product) preserving maps on Vf . Also we characterize the strongly zero-product (strongly Jordan zero-product) preserving maps on Vf in the case where V is a normed vector space and f is a continuous linear functional on V. Finally, for polynomials in one variable x over Vf , we shall show that each polynomial of precise degree n ≥ 0, with non-zero constant term has precisely n-zeros (counted with multiplicity) in Vf . While, polynomials of precise degree n ≥ 2, with zero constant term have infinitely many zeros when dim(V) ≥2. This shows that the algebraic fundamental theorem for polynomial equations over an arbitrary algebra, is not valid in general.
UR - http://www.kjm-math.org/article_12290.html
L1 - http://www.kjm-math.org/article_12290_710c39152e24a4b3dbb3fcee40265094.pdf
ER -