10 papers
Invertibility preserving mappings onto finite C*-algebras
Martin Mathieu, Francois Schulz
We prove that every surjective unital linear mapping which preserves invertible elements from a Banach algebra onto a C*-algebra carrying a faithful tracial state is a Jordan homom…
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…
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…