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Research Paper | Mathematics | India | Volume 8 Issue 8, August 2019

Some Spectral Properties of the Banach Algebra A ?d B with the Direct-Sum Product

H. V. Dedania | H. J. Kanani

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

Edition: Volume 8 Issue 8, August 2019,

Pages: 318 - 323