Some Spectral Properties of the Banach Algebra A ?d B with the Direct-Sum Product
Abstract: Let A be a commutative Banach algebra and B be a closed subalgebra of A. Then A B is a commutative algebra with co-ordinatewise linear operations and the direct-sum product: (a; b) (c; d) = (ac + ad + bc; bd) (a; c 2 A; b; d 2 B). In fact, it is a Banach algebra with a suitable norm; it is denoted by A d B. Here, we study some important spectral properties of this algebra.
Keywords: Banach algebras, Direct-sum product, Spectrum, Spectral radius, Spectral extension property, Gel'fand space, and Gel?fand transform
How to Cite?: H. V. Dedania, H. J. Kanani, "Some Spectral Properties of the Banach Algebra A ?d B with the Direct-Sum Product", Volume 8 Issue 8, August 2019, International Journal of Science and Research (IJSR), Pages: 318-323, https://www.ijsr.net/getabstract.php?paperid=ART2020185, DOI: https://dx.doi.org/10.21275/ART2020185