In this paper we show that the nilpotent perturbation of operators in the Helton class of p-hyponormal operators has scalar extensions. As a corollary we get that the nilpotent perturbation of each operator in the Helton class of p-hyponormal operators has a nontrivial invariant subspace if its spectrum has nonempty interior in the plane.
Bibliographical noteFunding Information:
This work is supported by a grant (R14-2003-006-01000-0) from the Korea Research Foundation. Corresponding author. E-mail addresses: firstname.lastname@example.org (I. Kim), email@example.com (Y. Kim), firstname.lastname@example.org (E. Ko), email@example.com (J.E. Lee).
- Helton class
- Subscalar operators
- p-Hyponormal operators