Weyl's theorem for upper triangular operator matrix and perturbations. Issue 7 (3rd July 2018)

• Record Type: Journal Article
• Authors: Cui, Miaomiao; Cao, Xiaohong
• Is Part Of: Linear & multilinear algebra. Volume 66:Issue 7(2018)
• Page Start: 1299
• Page End: 1310
• Publication Date: 2018-07-03
• Subjects: Weyl's theorem -- spectrum -- invariant subset -- upper triangular operator; 47B53 -- 47A55 -- 47A10; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1351516
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract: Let and be infinite dimensional separable complex Hilbert spaces and T a bounded linear operator on . 'Weyl's theorem' holds for operator T when the complement in the spectrum of the Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. Let . In this paper, we characterize the invariant subset and the diagonal operator matrix satisfying upper triangular operator matrix, where .