Repeated eigenvectors and the numerical range of self-adjoint quadratic operator polynomials |
| |
Authors: | Peter Lancaster Alexander S Markus Panayiotis Psarrakos |
| |
Institution: | (1) Department of Mathematics and Statistics, University of Calgary, T2L 1B4 Calgary, AB, Canada;(2) Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel;(3) Department of Mathematics, National Technical University, Zografou Campus, 15780 Athens, Greece |
| |
Abstract: | LetL() be a self-adjoint quadratic operator polynomial on a Hilbert space with numerical rangeW(L). The main concern of this paper is with properties of eigenvalues on W(L). The investigation requires a careful discussion of repeated eigenvectors of more general operator polynomials. It is shown that, in the self-adjoint quadratic case, non-real eigenvalues on W(L) are semisimple and (in a sense to be defined) they are normal. Also, for any eigenvalue at a point on W(L) where an external cone property is satisfied, the partial multiplicities cannot exceed two. |
| |
Keywords: | 47A12 47A75 15A60 |
本文献已被 SpringerLink 等数据库收录! |
|