### Abstract

It is shown that if $11$, the operator $I+T$ attains its norm. A reflexive Banach space $X$ and a bounded rank one operator $T$ on
$X$ are constructed such that $\|I+T\|>1$ and $I+T$ does not attain its norm.

Original language | English |
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Pages (from-to) | 115-136 |

Number of pages | 22 |

Journal | Integral Equations and Operator Theory |

Volume | 64 |

Issue number | 1 |

Publication status | Published - May 2009 |

### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis

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## Cite this

Shkarin, S. (2009). Norm attaining operators and pseudospectrum.

*Integral Equations and Operator Theory*,*64*(1), 115-136.