Abstract and Applied Analysis

Quasi-Jordan Banach Algebras

Reem K. Alhefthi, Akhlaq A. Siddiqui, and Fatmah B. Jamjoom

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We initiate a study of quasi-Jordan normed algebras. It is demonstrated that any quasi-Jordan Banach algebra with a norm 1 unit can be given an equivalent norm making the algebra isometrically isomorphic to a closed right ideal of a unital split quasi-Jordan Banach algebra; the set of invertible elements may not be open; the spectrum of any element is nonempty, but it may be neither bounded nor closed and hence not compact. Some characterizations of the unbounded spectrum of an element in a split quasi-Jordan Banach algebra with certain examples are given in the end.

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Abstr. Appl. Anal., Volume 2014 (2014), Article ID 690806, 11 pages.

First available in Project Euclid: 2 October 2014

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Alhefthi, Reem K.; Siddiqui, Akhlaq A.; Jamjoom, Fatmah B. Quasi-Jordan Banach Algebras. Abstr. Appl. Anal. 2014 (2014), Article ID 690806, 11 pages. doi:10.1155/2014/690806. https://projecteuclid.org/euclid.aaa/1412273274

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