### Abstract

Composition operators on the Hilbert Hardy space H^{2} whose symbols are analytic selfmaps of the open unit disk having orthogonal powers are considered. The spectra and essential spectra of such operators are described. In the general case of an arbitrary analytic selfmap of the open unit disk, it is proved that the composition operator induced by that map has essential spectral radius less than 1 if and only if the map under consideration is a non-inner map with a fixed point in the unit disk. The canonical decomposition of a non-unitary composition contraction is determined.

Original language | English (US) |
---|---|

Pages (from-to) | 845-857 |

Number of pages | 13 |

Journal | Houston Journal of Mathematics |

Volume | 37 |

Issue number | 3 |

State | Published - Dec 26 2011 |

### Fingerprint

### Keywords

- Composition operator
- Rudin's orthogonality condition

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Houston Journal of Mathematics*,

*37*(3), 845-857.

**Composition operators whose symbols have orthogonal powers.** / Matache, Valentin.

Research output: Contribution to journal › Article

*Houston Journal of Mathematics*, vol. 37, no. 3, pp. 845-857.

}

TY - JOUR

T1 - Composition operators whose symbols have orthogonal powers

AU - Matache, Valentin

PY - 2011/12/26

Y1 - 2011/12/26

N2 - Composition operators on the Hilbert Hardy space H2 whose symbols are analytic selfmaps of the open unit disk having orthogonal powers are considered. The spectra and essential spectra of such operators are described. In the general case of an arbitrary analytic selfmap of the open unit disk, it is proved that the composition operator induced by that map has essential spectral radius less than 1 if and only if the map under consideration is a non-inner map with a fixed point in the unit disk. The canonical decomposition of a non-unitary composition contraction is determined.

AB - Composition operators on the Hilbert Hardy space H2 whose symbols are analytic selfmaps of the open unit disk having orthogonal powers are considered. The spectra and essential spectra of such operators are described. In the general case of an arbitrary analytic selfmap of the open unit disk, it is proved that the composition operator induced by that map has essential spectral radius less than 1 if and only if the map under consideration is a non-inner map with a fixed point in the unit disk. The canonical decomposition of a non-unitary composition contraction is determined.

KW - Composition operator

KW - Rudin's orthogonality condition

UR - http://www.scopus.com/inward/record.url?scp=84055213043&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84055213043&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84055213043

VL - 37

SP - 845

EP - 857

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

SN - 0362-1588

IS - 3

ER -