Abstract
Let $$r_A(T)$$ denote the A-spectral radius of an operator T which is bounded with respect to the seminorm induced by a positive operator A on a complex Hilbert space $${\mathcal {H}}$$ . In this paper, we aim to establish several A-spectral radius inequalities for products, sums and commutators of A-bounded operators. Some applications of our results are provided. Moreover, we give an affirmative answer to the question recently posed by Baklouti and Namouri (Banach J Math Anal 16:12, https://doi.org/10.1007/s43037-021-00167-1 , 2022) regarding the connection between the notions of A-spectral radius and A-spectrum for A-bounded operators.
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