@article {
author = {Khoddami, Ali Reza},
title = {Strongly Zeo-product Preserving Maps on Normed Algebras Induced by a Bounded Linear Functional},
journal = {Khayyam Journal of Mathematics},
volume = {1},
number = {1},
pages = {107-114},
year = {2015},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2015.12290},
abstract = {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.},
keywords = {(Jordan) zero-product preserving map,strongly (Jordan) zeroproduct preserving map,Arens product,polynomial equation},
url = {http://www.kjm-math.org/article_12290.html},
eprint = {http://www.kjm-math.org/article_12290_710c39152e24a4b3dbb3fcee40265094.pdf}
}