Ideals of compact operators with Nakano type norms in a Hilbert space

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2 Scopus citations


Let H be a separable Hilbert space with a norm {double pipe}.{double pipe} H. For a compact linear operator A acting in H, let λ k(A) be the eigenvalues, s k(A) (k = 1,2, ...) singular values and {double pipe}A{double pipe} H = sup x∈H{double pipe}Ax{double pipe} H{double pipe}x{double pipe} H. Let π = {p k} k=1 be a nondecreasing sequence of numbers p k ≥ 1. Put We investigate the ideal X π of operators satisfying γ π (tA) < ∞ for all t > 0. In particular, it is proved that for any A ∈ X π we have where A = {double pipe}A{double pipe} H if {double pipe}A{double pipe} H > 1 and ν A = 1 if {double pipe}A{double pipe} H ≤ 1.

Original languageEnglish
Pages (from-to)493-494
Number of pages2
JournalOperators and Matrices
Issue number3
StatePublished - 1 Sep 2012


  • Compact operators
  • Estimates for eigenvalues
  • Hilbert space

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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