## Annals of Functional Analysis

- Ann. Funct. Anal.
- Volume 5, Number 1 (2014), 51-55.

### Some Banach algebra properties in the Cartesian product of Banach algebras

H. V. Dedania and H. J. Kanani

#### Abstract

For semisimple, commutative Banach algebras $\mathcal A$ and $\mathcal B$, some Banach algebra properties of the Cartesin product $\mathcal A \times \mathcal B$ are characterized in terms of $\mathcal A$ and $\mathcal B$. A couple of results are also proved for non-commutative Banach algebras.

#### Article information

**Source**

Ann. Funct. Anal., Volume 5, Number 1 (2014), 51-55.

**Dates**

First available in Project Euclid: 5 February 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.afa/1391614568

**Digital Object Identifier**

doi:10.15352/afa/1391614568

**Mathematical Reviews number (MathSciNet)**

MR3119111

**Zentralblatt MATH identifier**

1290.46045

**Subjects**

Primary: 46J05: General theory of commutative topological algebras

Secondary: 46K05: General theory of topological algebras with involution

**Keywords**

Banach algebra Cartesian product UUNP TAP SEP

#### Citation

Dedania, H. V.; Kanani, H. J. Some Banach algebra properties in the Cartesian product of Banach algebras. Ann. Funct. Anal. 5 (2014), no. 1, 51--55. doi:10.15352/afa/1391614568. https://projecteuclid.org/euclid.afa/1391614568