On matching distance between eigenvalues of unbounded operators

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3 Scopus citations


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 languageEnglish
Pages (from-to)46-53
Number of pages8
JournalConstructive Mathematical Analysis
Issue number1
StatePublished - 1 Jan 2022


  • Banach space
  • differential operator
  • matching distance
  • perturbations of eigenvalues
  • tensor product of Hilbert spaces

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics


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