Year: 2025
Type: article
Abstract: As a follow-up to D. Petz and J. Zemánek [1], and the methods of the authors in [7] we show a number of equivalent conditions which characterize the trace among linear functionals on ordered matrix algebras, finite rank operators and the ordered socle elements of semi simple, Banach algebras in general [7]. Investigate the converse problem; that is, given the equivalence of certain conditions which characterize the trace, what can be said about the structure of the socle? Hence, we characterize those socles isomorphic to ordered matrix algebras, as well as those ordered socles which are minimal two-sided ideals.
Authors: Radia I Humaida, Shawgy Hussein
Institution: Sudan University of Science and Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4408947870