ON WEYL AND BROWDER SPECTRA OF TENSOR PRODUCTS

Abstract

AbstractLet A and B be Hilbert space operators. In this paper we explore the structure of parts of the spectrum of the tensor product A ⊗ B, and conclude some properties that follow from such a structure. We give conditions on A and B ensuring that σw(A ⊗ B) =σw(A)ċσ(B) ∪ σ(A)ċσw(B), where σ(ċ) and σw(ċ) stand for the spectrum and Weyl spectrum, respectively. We also investigate the problem of transferring Weyl and Browder's theorems from A and B to their tensor product A⊗B.