Abstract
It is shown that if φ is a univalent self-map on the unit disk double-struck D sign is not an automorphism and has a fixed point in double-struck D sign and if the essential spectral radius of the composition operator C φ on H 2 is different from zero, then the spectrum of C φ on BMOA coincides with double-struck D sign̄. This answers in the affirmative a conjecture by MacCluer and Saxe.
| Original language | English |
|---|---|
| Pages (from-to) | 75-86 |
| Number of pages | 12 |
| Journal | Integral Equations and Operator Theory |
| Volume | 53 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Sept 2005 |
| MoE publication type | A1 Journal article-refereed |
Funding
The research of the authors was partially supported by the Academy of Finland Project No. 51906; the research of this paper was carried out while these authors were visiting Kent State University, whose hospitality is acknowledged with thanks.
Keywords
- BMOA
- Essential norm
- Essential spectral radius
- N
- Spectrum
- Weighted composition operator