Generalized a-Weyl's theorem for direct sums

摘要

If T and S are Hilbert space operators obeying generalized a-Weyl's theorem, then it does not necessarily imply that the direct sum T ⊕ S obeys generalized a-Weyl's theorem. In this paper we explore certain conditions on T and S so that the direct sum T ⊕ S obeys generalized a-Weyl's theorem.