Various Spectral Properties in the Banach Algebra $\mathcal A \times_{c} \mathcal I$ with the Convolution Product


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Authors

  • H. V. Dedania Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Gujarat, India
  • H. J. Kanani Department of Mathematics, Bahauddin Science College, Junagadh, Gujarat, India

Keywords:

Banach algebras, Convolution product, Topological divisor of zero, Quasi divisor of zero, Topological annihilator condition, Multiplicative Hahn-Banach property, Ditkin's condition, Tauberian condition

Abstract

Let $\mathcal I$ be an ideal of an associative algebra $\mathcal A$ over the field $\mathbb C$. Then the vector space $\mathcal A \times \mathcal I$ with pointwise linear operations becomes an algebra with the product $(a, x) (b, y) = (ab+xy, ay+bx) \; ((a, x), (b, y) \in \mathcal A \times \mathcal I).$ This product is known as the convolution product and this algebra is denoted by $\mathcal A \times_{c} \mathcal I$. In this paper, some well-known spectral properties of Banach algebras are studied for $\mathcal A \times_{c} \mathcal I$.

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Published

15-12-2019

How to Cite

H. V. Dedania, & H. J. Kanani. (2019). Various Spectral Properties in the Banach Algebra $\mathcal A \times_{c} \mathcal I$ with the Convolution Product. International Journal of Mathematics And Its Applications, 7(4), 9–14. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/199

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Section

Research Article