Fredholm theory in ordered Banach algebras. Issue 5 (11th August 2016)

• Record Type: Journal Article
• Authors: Benjamin, Ronalda; Mouton, Sonja
• Is Part Of: Quaestiones mathematicae. Volume 39:Issue 5(2016)
• Page Start: 643
• Page End: 664
• Publication Date: 2016-08-11
• Subjects: 46H05 -- 47A10 -- 47B65; Fredholm -- Weyl and Browder theory -- ordered Banach algebra -- upper Weyl and upper Browder theory; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2016.1167134
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: This paper illustrates some initial steps taken in the effort of unifying the theory of positivity in ordered Banach algebas (OBAs) with the general Fredholm theory in Banach algebras. We introduce here upper Weyl and upper Browder elements in an OBA relative to an arbitrary Banach algebra homomorphism and investigate the spectra corresponding to the sets of upper Weyl and upper Browder elements, which we shall refer to as the upper Weyl and upper Browder spectra, respectively.