Some properties of the Wolf and Weyl essential spectra of a sequence of linear operators ν-convergent

This work is devoted to the investigation of some properties of the essential spectra of a sequence of bounded linear operators by referring back to ν-convergence in a Banach space. In addition to that, we shed light on the notion of ν-continuity. In fact, if U is a bounded linear operator then the Wolf essential spectrum and the Weyl essential spectrum of U are ν-upper semi-continuous at U (Theorem 3.3). Similarly we study the ν-continuity of some 2×2 block operator matrices (Theorem 3.4).