The characterization and stability of extended eigenvalue
Hong-Ke Du · Basic Sciences Journal of Textile Universities · 2008
Let A be a bounded linear operator on a complex Hilbert space H.λ∈C is called an extended eigenvalue of A if there exists a nonzero operator B on H such that AB=λBA.The set of all extended eigenvalues of A is denoted by Σ(A).By using the technique of operator block,the extended eigenvalue of upper triangular operator matrices was studied.And more,it is showed that if A≥0 and A is invertible,then Σ(An/m)=(Σ(A))n/m,where n,m∈Z,and m≠0.