| Title:
|
Essential normality for certain finite linear combinations of linear-fractional composition operators on the Hardy space $H^{2}$ (English) |
| Author:
|
Fatehi, Mahsa |
| Author:
|
Robati, Bahram Khani |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
901-917 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In 1999 Nina Zorboska and in 2003 P. S. Bourdon, D. Levi, S. K. Narayan and J. H. Shapiro investigated the essentially normal composition operator $C_{\varphi }$, when $\varphi $ is a linear-fractional self-map of $\mathbb {D}$. In this paper first, we investigate the essential normality problem for the operator $T_{w}C_{\varphi }$ on the Hardy space $H^{2}$, where $w$ is a bounded measurable function on $\partial \mathbb {D}$ which is continuous at each point of $F(\varphi )$, $\varphi \in {\cal S}(2)$, and $T_{w}$ is the Toeplitz operator with symbol $w$. Then we use these results and characterize the essentially normal finite linear combinations of certain linear-fractional composition operators on $H^{2}$. (English) |
| Keyword:
|
Hardy spaces |
| Keyword:
|
essentially normal |
| Keyword:
|
composition operator |
| Keyword:
|
linear-fractional transformation |
| MSC:
|
30H10 |
| MSC:
|
46E20 |
| MSC:
|
47B33 |
| MSC:
|
47B35 |
| idZBL:
|
Zbl 1262.47052 |
| idMR:
|
MR3010247 |
| DOI:
|
10.1007/s10587-012-0073-y |
| . |
| Date available:
|
2012-11-10T21:29:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143035 |
| . |
| Reference:
|
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| Reference:
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