caa a22 4500 467931712 CHVBK 20180406152945.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s00020-005-1381-5 doi (NATIONALLICENCE)springer-10.1007/s00020-005-1381-5 Integral Equations and Operator Theory [Elektronische Daten] [Animikh Biswas, Srdjan Petrovic] Abstract.: A complex number λ is an extended eigenvalue of an operator A if there is a nonzero operator X such that AX=λ XA. 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. Birkhäuser Verlag, Basel, 2006 Extended eigenvalues nationallicence C 0 contraction nationallicence Biswas Animikh Department of Mathematics and Statistics, UNC - Charlotte, 28223, Charlotte, NC, USA aut Petrovic Srdjan Department of Mathematics, Western Michigan University, 49008, Kalamazoo, MI, USA aut Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 55/2(2006-06-01), 233-248 0378-620X 55:2<233 2006 55 20 https://doi.org/10.1007/s00020-005-1381-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-005-1381-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Biswas Animikh Department of Mathematics and Statistics, UNC - Charlotte, 28223, Charlotte, NC, USA aut NATIONALLICENCE 700 1- Petrovic Srdjan Department of Mathematics, Western Michigan University, 49008, Kalamazoo, MI, USA aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 55/2(2006-06-01), 233-248 0378-620X 55:2<233 2006 55 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer