Inequalities of the Carleman type for Schatten-von Neumann operators

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Abstract

Let S p be the ideal of the Schatten-von Neumann operators with the norm N p. For an integer p ≥ 3 and an A ∈ S p, the inequalities of the type ||(I - A) -1det p(I - A)|| ≤ exp [a p N p p(A) + c p] are proved, where det p(I A) is the regularized determinant, I is the unit operator and a p, and b p are explicitly pointed constants. Applications of these inequalities to spectrum perturbations of operators, as well as to invertibility and positive invertibility of infinite matrices are also discussed.

Original languageEnglish
Pages (from-to)203-213
Number of pages11
JournalAsian-European Journal of Mathematics
Volume1
Issue number2
DOIs
StatePublished - 1 Jun 2008

Keywords

  • Schatten-von Neumann operators
  • determinant
  • infinite matrices
  • invertibility
  • positive invertibility
  • resolvent
  • spectrum perturbations

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