The boundary of theq-numerical range of a reducible matrix

Abstract

In this study, we provide an algorithm for the boundary of the q-numerical range of a reducible matrix. An example is given to show that the q-numerical range cannot be derived from the classical numerical range of matrices.

Perturbation of the q-numerical radius of a weighted shift operator

“…There have been a sequence of interesting papers with results related to the q-numerical range (cf. [1,[5][6][7]13,15,16,19,20]). In the case q = 1, Stout [18] gave a formula for the numerical radius of a general Hilbert-Schmidt class weighted shift operator, as the reciprocity of a minimal positive root of an entire analytic function.…”