Abstract and Applied Analysis

Quasi-Jordan Banach Algebras

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

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273274

Digital Object Identifier
doi:10.1155/2014/690806

Mathematical Reviews number (MathSciNet)
MR3191059

Zentralblatt MATH identifier
07022887

Citation

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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