## Quasitriangular $+$ small compact $=$ strongly irreducible

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- by You Qing Ji PDF
- Trans. Amer. Math. Soc.
**351**(1999), 4657-4673 Request permission

## Abstract:

Let $T$ be a bounded linear operator acting on a separable infinite dimensional Hilbert space. Let $\epsilon$ be a positive number. In this article, we prove that the perturbation of $T$ by a compact operator $K$ with $\Vert K\Vert <\epsilon$ can be strongly irreducible if $T$ is a quasitriangular operator with the spectrum $\sigma (T)$ connected. The Main Theorem of this article nearly answers the question below posed by D. A. Herrero. Suppose that $T$ is a bounded linear operator acting on a separable infinite dimensional Hilbert space with $\sigma (T)$ connected. Let $\epsilon >0$ be given. Is there a compact operator $K$ with $\Vert K\Vert <\epsilon$ such that $T+K$ is strongly irreducible?## References

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## Additional Information

**You Qing Ji**- Affiliation: Department of Mathematics, Jilin University, Changchun 130023, P.R. China
- Received by editor(s): May 23, 1997
- Published electronically: July 20, 1999
- Additional Notes: This work is supported by MCSEC
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**351**(1999), 4657-4673 - MSC (1991): Primary 47A10, 47A55, 47A58
- DOI: https://doi.org/10.1090/S0002-9947-99-02307-7
- MathSciNet review: 1603910