An observation about normaloid operators
Jor-Ting Chan, Kong Chan · Operators and Matrices · 2017
Let H be a complex Hilbert space and B(H) the Banach space of all bounded linear operators on H .For any A ∈ B(H) , let w(A) denote the numerical radius of A .Then A is normaloid if w(A) = A .In this note, we show that A is normaloid if there is a sequence of unit vectors (x n ) such that lim n→∞ Ax n = A and lim n→∞