Fredholm theory in ordered Banach algebras

Benjamin, Ronalda; Mouton, S.

doi:10.2989/16073606.2016.1167134

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Cited by 9 publications

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“…In the early 1980's Harte [10] introduced Fredholm, Weyl and Browder theory relative to a unital homomorphism T : A → B between general unital Banach algebras A and B. Several authors have continued this investigation (see [11], [12], [18], [19], [15], [17], [4] and [5]).…”

Section: Introductionmentioning

confidence: 99%

r-FREDHOLM THEORY IN BANACH ALGEBRAS

Benjamin¹,

Laustsen²,

Mouton³

2018

Glasgow Math. J.

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Harte (1982, Math. Z. 179, 431–436) initiated the study of Fredholm theory relative to a unital homomorphism T: A → B between unital Banach algebras A and B based on the following notions: an element a ∈ A is called Fredholm if 0 is not in the spectrum of Ta, while a is Weyl (Browder) if there exist (commuting) elements b and c in A with a = b + c such that 0 is not in the spectrum of b and c is in the null space of T. We introduce and investigate the concepts of r-Fredholm, r-Weyl and r-Browder elements, where 0 in these definitions is replaced by the spectral radii of a and b, respectively.

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