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On regularities and Fredholm theory

L. Lindeboom, H. Raubenheimer (2002)

Czechoslovak Mathematical Journal

We investigate the relationship between the regularities and the Fredholm theory in a Banach algebra.

On topological algebras

G. A. Stavrakas (1991)

Πανελλήνιο Συνέδριο Μαθηματικής Παιδείας

Range inclusion results for derivations on noncommutative Banach algebras

Volker Runde (1993)

Studia Mathematica

Let A be a Banach algebra, and let D : A → A be a (possibly unbounded) derivation. We are interested in two problems concerning the range of D: 1. When does D map into the (Jacobson) radical of A? 2. If [a,Da] = 0 for some a ∈ A, is Da necessarily quasinilpotent? We prove that derivations satisfying certain polynomial identities map into the radical. As an application, we show that if [a,[a,[a,Da]]] lies in the prime radical of A for all a ∈ A, then D maps into the radical. This generalizes a result...

Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems

Gareth Braatvedt, Rudolf Brits, Francois Schulz (2015)

Studia Mathematica

As a follow-up to a paper of Aupetit and Mouton (1996), we consider the spectral definitions of rank, trace and determinant applied to elements in a general Banach algebra. We prove a generalization of Sylvester's Determinant Theorem to Banach algebras and thereafter a generalization of the Frobenius inequality.

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