On q-Numerical Ranges of Operators

Abstract

In this paper, we study the properties of the q-numerical ranges Wq(T) for an operator T∈L(H). In particular, if T∗ is similar to T or T-1 via an invertible operator X∈L(H), respectively, where 0∉Wq(X-1)¯, we investigate the spectrum of T and properties of T. Moreover, we prove that if T is compact and 0∈Wq(T), then Wq(T) is closed. Furthermore, we study about the continuity of Wq(·)¯ and the Hausdorff distance. Finally, we consider properties of q-numerical ranges for special classes of operators. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2026.