Lower bounds for eigenvalues of Schatten-von Neumann operators

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11 Scopus citations


Let Sp be the Schatten-von Neumann ideal of compact operators equipped with the norm Np(·). For an A ∈ Sp, (1 < p < ∞), the inequality [∑k=1 | Re λk(A) |p]1/p + bp [∑k=1 | Im λk(A)| p]1/p ≥ Np(AR) - b pNp(AI) (bp = const. > 0) is derived, where λj(A) (j = 1, 2, . . .) are the eigenvalues of A, AI = (A - A*)/2i and AR = (A + A*)/2. The suggested approach is based on some relations between the real and imaginary Hermitian components of quasinilpotent operators.

Original languageEnglish
Article number66
JournalJournal of Inequalities in Pure and Applied Mathematics
Issue number3
StatePublished - 22 Oct 2007


  • Inequalities for eigenvalues
  • Schatten-von Neumann ideals

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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