Joint normality of operators in semi-Hilbertian spaces

• Published in: Linear & multilinear algebra Vol. 68; no. 4; pp. 845 - 866
• Main Authors: Baklouti, Hamadi, Feki, Kais, Ould Ahmed Mahmoud, Sid Ahmed
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.04.2020; Taylor & Francis Ltd
• Subjects: Hilbert space; joint numerical range; joint spectral radius; Linear operators; Mathematical analysis; Normality; Positive operator; Primary 46C05; Secondary 47A05; semi-inner products; Tensors

In this paper, we introduce the concept of normality of a d-tuple of bounded linear operators acting on a complex Hilbert space when an additional semi-inner product induced by a positive operator A is considered. We investigate this new class of operators which is called A-normal d-tuple of operato...