On inequalities for eigenvalues of 2 × 2 matrices with Schatten–von Neumann entries

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Abstract

Let SNr (r ≥ 1) denote the Schatten-von Neumann ideal of compact operators in a separable Hilbert space. For the block matrix (Formula presented.) the inequality (Formula presented.) (p = 2; 3; … ) is proved, where λk(A) (k = 1; 2; … ) are the eigenvalues of A and Nr(.) is the norm in SNr. Moreover, let P(z) = z2I + Bz + C (z ∈ ℂ) with B ∈ SN2p, C ∈ SNp. By zk(P) (k = 1; 2; … ) the characteristic values of the pencil P are denoted. It is shown that (Formula presented.) In the case p = 1, sharper results are established. In addition, it is derived that (Formula presented.)

Original languageEnglish
Pages (from-to)145-152
Number of pages8
JournalQuaestiones Mathematicae
Volume39
Issue number2
DOIs
StatePublished - 31 Mar 2016

Keywords

  • Operator matrix
  • Schatten-von Neumann operators
  • eigenvalues
  • operator pencil

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