Generalized Browder's theorem for tensor product and elementary operators

TL;DR

This paper characterizes the transfer property of the generalized Browder's theorem for tensor product and elementary operators, focusing on spectrum inclusion and isolated points.

Contribution

It provides a complete characterization of the transfer property and isolated points for these operators in terms of B-Weyl spectrum inclusion.

Findings

Transfer property characterized via B-Weyl spectrum inclusion.

Isolated points of tensor product and elementary operators fully characterized.

Conditions established for the transfer property in these operators.

Abstract

The transfer property for the generalized Browder's theorem both of the tensor product and of the left-right multiplication operator will be characterized in terms of the $B$-Weyl spectrum inclusion. In addition, the isolated points of these two classes of operators will be fully characterized.