Abstract
Let A and à be linear operators on a Banach space having compact resolvents, and let λk(A) and λk(Ã) (k = 1, 2, ...) be the eigenvalues taken with their algebraic multiplicities of A and Ã, respectively. Under some conditions, we derive a bound for the quantity md(A, Ã):= inf sup |λπ(k)(Ã) − λk(A)|, π k=1,2,... where π is taken over all permutations of the set of all positive integers. That quantity is called the matching optimal distance between the eigenvalues of A and Ã. Applications of the obtained bound to matrix differential operators are also discussed.
Original language | English |
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Pages (from-to) | 46-53 |
Number of pages | 8 |
Journal | Constructive Mathematical Analysis |
Volume | 5 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2022 |
Keywords
- Banach space
- differential operator
- matching distance
- perturbations of eigenvalues
- tensor product of Hilbert spaces
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Applied Mathematics