Weyl’s theorem, a-weyl’s theorem and single-valued extension property

Abstract

In this paper we investigate the relation of Weyl’s theorem, of a-Weyl’s theorem and the single valued extension property. In particular, we establish necessary and sufficient conditions for a Banach space operator 𝑇 to satisfy Weyl’s theorem or a-Weyl’s theorem, in the case in which 𝑇, or its dual 𝑇 *, has the single valued extension property. These results improve similar results obtained by Curto and Han, Djordjevic S. V., Duggal B. P., and Y. M. Han. The theory is exemplified in the case of multipliers of commutative semi-simple Banach algebras, in particular convolution operators on the group algebra L¹(𝙶), weighted shift operators on ℓᴾ(ℕ), with 1 ≤ 𝑝 < ∞, as well as other classes of operators