We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
AN INEQUALITY FOR IMAGINARY PARTS OF EIGENVALUES OF NON-COMPACT OPERATORS WITH HILBERT-SCHMIDT HERMITIAN COMPONENTS.
- Authors
Gil', Michael
- Abstract
Let A be a bounded linear operator in a complex separable Hilbert space, A* be its adjoint one and AI := (A - A*)/(2i). Assuming that AI is a Hilbert-Schmidt operator, we investigate perturbations of the imaginary parts of the eigenvalues of A. Our results are formulated in terms of the "extended" eigenvalue sets in the sense introduced by T. Kato. Besides, we refine the classical Weyl inequality P 8k =1(Im k(A))2 = N2 2 (AI), where k(A) (k = 1, 2, . . .) are the eigenvalues of A and N2(·) is the Hilbert-Schmidt norm. In addition, we discuss applications of our results to the Jacobi operators.
- Subjects
HERMITIAN operators; JACOBI operators; EIGENVALUES; HILBERT space
- Publication
Opuscula Mathematica, 2024, Vol 44, Issue 2, p241
- ISSN
1232-9274
- Publication type
Article
- DOI
10.7494/OpMath.2024.44.2.241