International Journal of Science and Research (IJSR)

International Journal of Science and Research (IJSR)
Call for Papers | Fully Refereed | Open Access | Double Blind Peer Reviewed

ISSN: 2319-7064


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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


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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), Volume 8 Issue 8, August 2019, pp. 318-323, https://www.ijsr.net/get_abstract.php?paper_id=ART2020185

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