Abstract
For bounded linear operators defined on complex infinite-dimensional Banach space, H. Zariouh, in an article [1] 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.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
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