13 papers
Some Character Generating Functions on Banach Algebras
R. Brits, F. Schulz, C. Toure
We consider a multiplicative variation on the classical Kowalski-Słodkowski Theorem which identifies the characters among the collection of all functionals on a Banach algebra .…
The Shoda-completion of a Banach algebra
Rudi Brits, Francois Schulz
In stark contrast to the case of finite rank operators on a Banach space, the socle of a general, complex, semisimple, and unital Banach algebra may exhibit the `pathological'…
Commutators, Commutativity and Dimension in the Socle of a Banach Algebra: A generalized Wedderburn-Artin and Shoda's Theorem
Rudi Brits, Francois Schulz
As a follow-up to work done in [7], some new insights to the structure of the socle of a semisimple Banach algebra is obtained. In particular, it is shown that the socle is isomorp…
Trace Characterizations and Socle Identifications in Banach Algebras
Gareth Braatvedt, Rudi Brits, Francois Schulz
As a follow-up to a paper of D. Petz and J. Zemánek [4], a number of equivalent conditions which characterize the trace among linear functionals on matrix algebras, finite rank ope…
A Spectral Characterization of Isomorphisms on -Algebras
Rudi Brits, Francois Schulz, Cheick Toure
Following a result of Hatori, Miura and Tagaki ([4]) we give here a spectral characterization of an isomorphism from a -algebra onto a Banach algebra. We then use this res…
Uniqueness under Spectral Variation in the Socle of a Banach Algebra
Rudi Brits, Francois Schulz
Let be a complex semisimple Banach algebra with identity, and denote by and the nonzero spectrum and spectral radius of an element , respectively. We ex…
Identities, Approximate Identities and Topological Divisors of Zero in Banach Algebras
Rudi Brits, Melanie Hasse, Francois Schulz
In [3] S. J. Bhatt and H. V. Dedania exposed certain classes of Banach algebras in which every element is a topological divisor of zero. We identify a new (large) class of Banach a…
Truncation and Spectral Variation in Banach Algebras
Rudi Brits, Francois Schulz, Cheick Toure
Let and be elements of a semisimple, complex and unital Banach algebra . Using subharmonic methods, we show that if the spectral containment holds…
Perturbation and Spectral Discontinuity in Banach Algebras
Rudi Brits
We extend an example of B. Aupetit, which illustrates spectral discontinuity for operators on an infinite dimensional separable Hilbert space, to a general spectral discontinuity r…
Applications of the Growth Characteristics Induced by the Spectral Distance
Rudi Brits
Let be a complex unital Banach algebra. Using a connection between the spectral distance and the growth characteristics of a certain entire map into , we derive a generaliza…
Finite Spectra and Quasinilpotent Equivalence in Banach Algebras
Rudi Brits, Heinrich Raubenheimer
This paper further investigates the implications of quasinilpotent equivalence for (pairs of) elements belonging to the socle of a semisimple Banach algebra. Specifically, not only…
Geometry of the Spectral Semidistance in Banach Algebras
Gareth Braatvedt, Rudi Brits
Let be a unital Banach algebra over , and suppose that the nonzero spectral values of, respectively, $a\mbox{ and }b\in A$ are discrete sets which cluster at $0\in\m…
Rank in Banach Algebras: A Generalized Cayley-Hamilton Theorem
Gareth Braatvedt, Rudi Brits, Francois Schulz
Let be a semisimple Banach algebra with non-trivial, and possibly infinite-dimensional socle. Addressing a problem raised by Harte and Hernandez, we first define a characterist…