| Title:
|
Separately radial and radial Toeplitz operators on the projective space and representation theory (English) |
| Author:
|
Quiroga-Barranco, Raul |
| Author:
|
Sanchez-Nungaray, Armando |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
4 |
| Year:
|
2017 |
| Pages:
|
1005-1020 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider separately radial (with corresponding group ${\mathbb {T}}^n$) and radial (with corresponding group ${\rm U}(n))$ symbols on the projective space ${\mathbb {P}^n({\mathbb {C}})}$, as well as the associated Toeplitz operators on the weighted Bergman spaces. It is known that the $C^*$-algebras generated by each family of such Toeplitz operators are commutative (see R. Quiroga-Barranco and A. Sanchez-Nungaray (2011)). We present a new representation theoretic proof of such commutativity. Our method is easier and more enlightening as it shows that the commutativity of the $C^*$-algebras is a consequence of the existence of multiplicity-free representations. Furthermore, our method shows how to extend the current formulas for the spectra of the corresponding Toeplitz operators to any closed group lying between ${\mathbb {T}}^n$ and ${\rm U}(n)$. (English) |
| Keyword:
|
Toeplitz operator |
| Keyword:
|
projective space |
| MSC:
|
22E46 |
| MSC:
|
32A36 |
| MSC:
|
32M15 |
| MSC:
|
47B35 |
| idZBL:
|
Zbl 06819569 |
| idMR:
|
MR3736015 |
| DOI:
|
10.21136/CMJ.2017.0293-16 |
| . |
| Date available:
|
2017-11-20T14:55:15Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146963 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Quiroga-Barranco, R., Sanchez-Nungaray, A.: Commutative $C^*$-algebras of Toeplitz operators on complex projective spaces.Integral Equations Oper. Theory 71 (2011), 225-243. Zbl 1251.47065, MR 2838143, 10.1007/s00020-011-1897-9 |
| Reference:
|
[9] Quiroga-Barranco, R., Vasilevski, N.: Commutative $C^*$-algebras of Toeplitz operators on the unit ball, I.: Bargmann-type transforms and spectral representations of Toeplitz operators.Integral Equations Oper. Theory 59 (2007), 379-419. Zbl 1144.47024, MR 2363015, 10.1007/s00020-007-1537-6 |
| Reference:
|
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| . |
