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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

Country: India, Subject Area: Mathematics

Pages: 318 - 323

Edition: Volume 8 Issue 8, August 2019

How to Cite this Article?

H. V. Dedania, H. J. Kanani, "Some Spectral Properties of the Banach Algebra A ?d B with the Direct-Sum Product", International Journal of Science and Research (IJSR), https://www.ijsr.net/archive/v8i8/show_abstract.php?id=ART2020185, Volume 8 Issue 8, August 2019, 318 - 323

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