Extending Polynomially Normal Operators to (P, Q)-Normal Operators in Semi-Hilbertian Spaces
Abstract
This paper is devoted to the introduction and systematic study of (P,Q)-normal operators in the context of semi-Hilbertian spaces, where P and Q are non-constant complex polynomials in one variable. This class generalizes the well-known notion of polynomially normal operators and offers a natural setting to study their structural properties in spaces endowed with a semi-inner product induced by a positive operator. We establish fundamental properties of (P,Q)-normal operators, including conditions for commutativity with respect to the A-adjoint and relations to other classes of A-operators. Several examples are provided to illustrate the theory and demonstrate how (P,Q)-normality extends classical concepts in operator theory.
Fields of Study & Subjects
Holomorphic and Operator Theory
Advanced Banach Space Theory
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Mathematics
- Publisher
- MDPI AG
- Volume
- 14
- Issue
- 5
- Pages
- 834–834
- Publication date
- 1 March 2026
- Language
- EN