Integral Equations and Operator Theory
Loading...
Links to Files
Collections
Author/Creator
Author/Creator ORCID
Date
2005-12-20
Type of Work
Department
Program
Citation of Original Publication
Biswas, Animikh, and Srdjan Petrovic. “Integral Equations and Operator Theory.” Integral Equations and Operator Theory 55, no. 2 (June 1, 2006): 233–48. https://doi.org/10.1007/s00020-005-1381-5.
Rights
This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
Abstract
A complex number λ is an extended eigenvalue of an operator A if there is a nonzero operator X such that AX = λXA. We characterize the set of extended eigenvalues, which we call extended point spectrum, for operators acting on finite dimensional spaces, finite rank operators, Jordan blocks, and C₀ contractions. We also describe the relationship between the extended eigenvalues of an operator A and its powers. As an application, we show that the commutant of an operator A coincides with that of Aⁿ, n ≥ 2, n ∈ N if the extended point spectrum of A does not contain any n–th root of unity other than 1. The converse is also true if either A or A* has trivial kernel.