Joint normality of operators in semi-Hilbertian spaces - Baklouti, Hamadi; Feki, Kais; Ould Ahmed Mahmoud, Sid Ahmed (Linear & multilinear algebra, 2020)
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 .