Theq-numerical ranges of normal operators
Mao-Ting Chien, Hiroshi Nakazato · Linear and Multilinear Algebra · 2005
Let T be a bounded linear operator on a complex Hilbert space H with inner product ⟨·, ·⟩. For a real number q ∈ [0, 1], the q-numerical range of T is defined by We obtain fundamental properties of the function h on conv(σ (T)) defined by If T is normal, these fundamental properties are applicable to show that Furthermore, if T is a non-essential hermitian then closure(Fq (T)) is the union of Fq (diag(λ1, λ2, λ3)) over distinct extreme points λ1, λ2, λ3 of conv(σ (T)).