Schurian Algebras and Spectral Additivity

  title={Schurian Algebras and Spectral Additivity},
  author={Lawrence A. Harris and Richard V. Kadison},
A class of algebras is introduced that includes the unital Banach algebras over the complex numbers. Commutator results are proved for such algebras and used to establish spectral properties of certain elements of Banach algebras. 1. Introduction. In this note, we introduce a condition on an algebra motivated by the situation in which Schur's lemma [S1] is applicable. We say that algebras satisfying this condition are Schurian. For such algebras, we prove some (purely algebraic) results… CONTINUE READING

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