Joint normality of operators in semi-Hilbertian spaces

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...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 68; no. 4; pp. 845 - 866
Main Authors Baklouti, Hamadi, Feki, Kais, Ould Ahmed Mahmoud, Sid Ahmed
Format Journal Article
LanguageEnglish
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
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Summary: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 operators. Mainly, we study the tensor product and the tensor sum of two A-normal d-tuples of operators. Also, we define the A-joint spectral radius associated with a d-tuple denoted and we show that under some conditions we have , where denotes the A-joint operator seminorm of .
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2019.1593925