On expansive operators that are quasisimilar to the unilateral shift of finite multiplicity
Year: 2025
Type: article
Abstract: An operator T on a Hilbert space H is called expansive, if ∥Tx∥⩾∥x∥ (x∈H). Expansive operators T quasisimilar to the unilateral shift of finite multiplicity N are studied. In particular, it is proved that I−T∗T is of trace class for such T and there exist invariant subspaces M of T such that the restriction T|M of T on M is similar to the unilateral shift of multiplicity 1. Such M span H, and the minimal number of such M which span H is N for N⩾2 and 2 for N=1.
Source: Journal of Operator Theory
Author: Maria Gamal
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4410363897