Finite rank perturbations of normal operators: spectral idempotents and decomposability Articles uri icon

publication date

  • December 2023


  • 12, 110148


  • 258

International Standard Serial Number (ISSN)

  • 0022-1236

Electronic International Standard Serial Number (EISSN)

  • 1096-0783


  • We prove that a large class of finite rank perturbations of diagonal operators and, in general, of diagonalizable normal operators of multiplicity one acting boundedly on a separable, infinite dimensional complex Hilbert space are decomposable operators in the sense of Colojoar¿ and Foia¿ [1]. Consequently, every operator T in such a class has a rich spectral structure and plenty of non-trivial closed hyperinvariant subspaces which extends, in particular, previous theorems of Foia¿, Jung, Ko and Pearcy [5], [6], [7], Fang and J. Xia [3] and the authors [8], [9] on an open question posed by Pearcy in the seventies.


  • Mathematics


  • finite rank perturbations of normal operators; invariant subspaces; spectral subspaces; decomposable operators