### Abstract

A bounded linear operator T∈L(X) acting on a Banach space satisfies property (w), a variant of Weyl’s theorem, if the complement in the approximate point spectrum σa(T) of the Weyl essential approximate-point spectrum σwa(T) is the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this note, we study the stability of property (w) for a polaroid operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operators and, more generally, by algebraic operators commuting with T.

Original language | English |
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Pages (from-to) | 1791-1802 |

Number of pages | 12 |

Journal | Linear Algebra and Its Applications |

Volume | 428 |

Publication status | Published - 2008 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

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## Cite this

Aiena, P., Guillen, J. R., & Peña, P. (2008). PROPERTY (w) FOR PERTURBATIONS OF POLAROID OPERATORS.

*Linear Algebra and Its Applications*,*428*, 1791-1802.