On the Single-Valued Extension Property of Hyponormal Operators on Banach Spaces

Abstract

In this paper, we study the single-valued extension property of hyponormal operators on Banach spaces $${\mathcal {X}}$$ . In particular, we prove that if a bounded linear operator T on $${\mathcal {X}}$$ has the property (II) or the property (I $$')$$ (see Definition 2.3), then T has the single-valued extension property. Moreover, we show that for strictly convex (resp., smooth) $$\mathcal {{\mathcal {X}}}$$ , if $$T\in {{\mathcal {L}}}(\mathcal {{\mathcal {X}}})$$ is hyponormal (resp., $$\,^*$$ -hyponormal) on $$\mathcal {{\mathcal {X}}}$$ , then T has the single-valued extension property.