DOIAbstract
AbstractLet f be a Lipschitz operator from a path-connected set D⊆Cm into Cm, with the lub-Lipschitz constant L(f) and the so-called “Gerschgorim range radius” r(f) subordinate to a given vector norm ∥·∥ of Cm. In 1986 [Numer. Math. 50 (1986) 27], Söderlind’s conjectured that if r(f)<L(f), then there exists a new vector norm ∥·∥* of Cm such that the induced lub-Lipschitz constant L*(f)⩽r(f). In this paper, we affirmatively prove Söderlind’s conjecture for several class of Lipschitz operators f, whilst we construct a counterexample to disprove Söderlind’s conjecture
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