Joint normality of operators in semi-Hilbertian spaces
By Hamadi Baklouti, Kais Feki, Sid Ahmed Ould Ahmed Mahmoud. Linear and multilinear algebra, 2020
67 citations recorded by the source corpus.
ABSTRACT 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 .
Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/016cb15b5c00127aa8a79528c4af55b5625a6ff0
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In Algebra and Number Theory
In Applied Mathematics
- Pintu Bhunia
- Kallol Paul
- Kais Feki
- Ali Zamani
- Mohammad Sal Moslehian
- Qingxiang Xu
- Janusz Brzdek
- Krzysztof Cieplinski
In Computational Theory and Mathematics
Citations in the corpus
- A-Numerical Radius Orthogonality and Parallelism of Semi-Hilbertian Space Operators and Their Applications (2020, background): “Several results covering some classes of operators on a Hilbert space H were extended when an additional semiinner product defined by A ∈ B(H)+ is considered, one may see [4,6,7,11,18,20,23].”
- Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces (2019, background): “Some other related topics can be found in [1, 2, 3, 4, 8, 9, 10, 11, 12, 13, 15, 17].”
- A note on the A-numerical radius of operators in semi-Hilbert spaces (2020, background): “The reader may refer to [3,4,7,12] and the references therein.”