### Arens-irregularity of tensor product of Banach algebras

Authors

Department of Mathematics, Persian Gulf University, Boushehr, 75168, Iran

Abstract

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

Keywords