Tensor Product of Operators Satisfying Zariouh’s Property (gaz), and Stability under Perturbations

Abstract

For bounded linear operators defined on complex infinite-dimensional Banach space, H. Zariouh, in an article (Property (gz) for bounded linear operators, (2013)) introduced and studied the property (gaz). In this study, through techniques using the local spectral theory of operators, we discover the sufficient conditions that allow the transfer of the property (gaz) from two tensor factors T and S to their tensor product T⊗S. The stability of the property (gaz) in the tensor product under perturbations is also investigated. The theory is exemplified by considering suitable classes of operators such as shift operators, convolution operators, and m-invertible contractions.

Property (Bv) and Tensor Product

“…Then, Duggal [19], Rashid [20] and Rashid and Prasad [21] continued these studies with Weyl and Browder type theorems. In addition, recently in [22,23] we can see a strong study linked to the tensor product of two operators.…”