## Abstract

For an integer p ≥ 1, let Γ_{p} be an approximative quasi-normed ideal of compact operators in a Banach space with a quasi-norm NΓ_{p}(.) and the property [formula presented] where λ_{k}(A) (k = 1, 2, ...) are the eigenvalues of A and a_{p} is a constant independent of A. Let A, Ã A Γ_{p} and [formula presented] where b_{p} is the quasi-triangle constant in Γ_{p}. It is proved the following result: let I be the unit operator, I - A^{p} be boundedly invertible and [formula presented] where ψ_{p}(A) = inf_{k=1,2,...} |1 - λkp $ begin{array}{} displaystyle λ k^{p} end{array}$(A)|. Then I - Ã^{p} is also boundedly invertible. Applications of that result to the spectrum perturbations of absolutely p-summing and absolutely (p, 2) summing operators are also discussed. As examples we consider the Hille-Tamarkin integral operators and matrices.

Original language | English |
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Pages (from-to) | 1025-1034 |

Number of pages | 10 |

Journal | Open Mathematics |

Volume | 17 |

Issue number | 1 |

DOIs | |

State | Published - 14 Sep 2019 |

## Keywords

- Banach space
- absolutely (p, 2)-summing operators
- absolutely p-summing operators
- compact operators
- infinite matrices
- integral operators
- perturbations

## ASJC Scopus subject areas

- General Mathematics