Advancing joint B-Weyl operators: Stability and spectral extensions in Banach spaces

In this paper, we introduce and investigate new classes of d -tuples of operators on Banach spaces, namely, the joint left and joint right B-Weyl operators. These notions represent a significant advancement in the study of d -tuples of operators and extend the recent work initiated in [A. Bahloul, Insights into a new class of unbounded operators, Georgian Math. J. 32 2025, 2, 211–218], by generalizing the concepts of left and right B-Weyl operators. Our approach focuses on analyzing the stability of these new classes under finite-rank and commuting quasi-nilpotent perturbations, thereby demonstrating their robustness in broader contexts. Furthermore, we establish novel spectral characterizations linking joint B-Weyl spectra to joint Drazin spectra. These results deepen the understanding of multivariable operator theory and extend classical results of B-Fredholm theory to the joint setting of left and right B-Weyl spectra.