3 papers
math.FA2018
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…
math.FA2018
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…
math.FA2018
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…