## Abstract

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 language | English |
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Pages (from-to) | 493-494 |

Number of pages | 2 |

Journal | Operators and Matrices |

Volume | 6 |

Issue number | 3 |

DOIs | |

State | Published - 1 Sep 2012 |

## Keywords

- Compact operators
- Estimates for eigenvalues
- Hilbert space

## ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory