Arens-irregularity of tensor product of Banach algebras


aDepartment of Mathematics, Persian Gulf University, Boushehr, 75168, Iran.


We introduce Banach algebras arising from tensor norms. By these Banach algebras we make Arens
regular Banach algebras such that tensor product becomes irregular, where is tensor norm. We
illustrate injective tensor product, does not preserve bounded approximate identity and it is not
algebra norm.