Trace characterizations and socle identifications in Banach algebras

F. Schulz, R. Brits, G. Braatvedt

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


As a follow-up to a paper of D. Petz and J. Zemánek [1], a number of equivalent conditions which characterize the trace among linear functionals on matrix algebras, finite rank operators and the socle elements of semisimple Banach algebras in general are given. Moreover, the converse problem is also addressed; that is, given the equivalence of certain conditions which characterize the trace, what can be said about the structure of the socle? In particular, we characterize those socles isomorphic to matrix algebras in this manner, as well as those socles which are minimal two-sided ideals.

Original languageEnglish
Pages (from-to)151-166
Number of pages16
JournalLinear Algebra and Its Applications
Publication statusPublished - 1 May 2015


  • Rank
  • Socle
  • Trace

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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