Continuity of the spectrum and Weyl type theorems for extension of 2-isometric operators

Abstract

In this paper, we show that the spectrum, Weyl spectrum, and Browder spectrum are continuous on the set of all 2-quasi-2-isometric operators. Further, we show that k-quasi-2-isometric operator satisfies Bishop's property β. Moreover, we prove Weyl type theorems for f(dTS), where dTS denote the generalized derivation or the elementary operator with k-quasi-2-isometric operator entries T and S* and f ∈ H(σ(dTS)), the set of analytic functions which are defined on an open neighborhood of σ(dTS).