Work

Generalized normal operators and the $\mathcal{P}$-absolute value of operators

Year: 2026

Type: article

Abstract: In this paper, a generalization of normal operators in Hilbert spaces is introduced. Specifically, a bounded linear operator T on a complex Hilbert space $\mathsf{H}$ as $[\mathcal{P}]$ -normal if $T^{*}\mathcal{P}T = T\mathcal{P}T^{*}$ is defined, where $\mathcal{P}$ is a bounded positive linear operator on $\mathsf{H}$ , and $T^{*}$ denotes the adjoint operator of T . Several properties and characterizations involving this new class of operators are examined. Additionally, the $\mathcal{P}$ -absolute value in semi-Hilbert spaces is introduced, and several applications are presented, including a generalization of the polar decomposition and Bohr’s inequality for Hilbert space operators. Other related results are also discussed.

Source: Journal of Inequalities and Applications

DOI: 10.1186/s13660-026-03532-6

Author: Najla Altwaijry

Institution: King Saud University

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,190

Funder: King Saud University