Perturbations of determinants of nuclear operators in a Hilbert space

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Abstract

Let (Figure presented.) be a complex separable Hilbert space with the unit operator I and {dk } be an orthonormal basis in (Figure presented.). Let A, Ã be linear operators in (Figure presented.), satisfying the conditions (Figure presented.). It is proved that the determinants satisfy the inequalities (Figure presented.) (Figure presented.). These inequalities refine the well-known ones and enable us to establish upper and lower bounds for the determinants of infinite matrices which are “close” to triangular matrices.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalQuaestiones Mathematicae
DOIs
StatePublished - 1 Jan 2020

Keywords

  • Hilbert space
  • determinants
  • nuclear operators
  • perturbations

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