| Title:
|
Complex symmetric weighted composition operators on the Hardy space (English) |
| Author:
|
Jiang, Cao |
| Author:
|
Han, Shi-An |
| Author:
|
Zhou, Ze-Hua |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
3 |
| Year:
|
2020 |
| Pages:
|
817-831 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper identifies a class of complex symmetric weighted composition operators on $H^2(\mathbb {D})$ that includes both the unitary and the Hermitian weighted composition operators, as well as a class of normal weighted composition operators identified by Bourdon and Narayan. A characterization of algebraic weighted composition operators with degree no more than two is provided to illustrate that the weight function of a complex symmetric weighted composition operator is not necessarily linear fractional. (English) |
| Keyword:
|
complex symmetry |
| Keyword:
|
weighted composition operator |
| Keyword:
|
Hardy space |
| MSC:
|
47B33 |
| MSC:
|
47B38 |
| idZBL:
|
07250692 |
| idMR:
|
MR4151708 |
| DOI:
|
10.21136/CMJ.2020.0555-18 |
| . |
| Date available:
|
2020-09-07T09:40:29Z |
| Last updated:
|
2022-10-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148331 |
| . |
| Reference:
|
[1] Bourdon, P. S., Narayan, S. K.: Normal weighted composition operators on the Hardy space $H^2(\mathbb{U})$.J. Math. Anal. Appl. 367 (2010), 278-286. Zbl 1195.47013, MR 2600397, 10.1016/j.jmaa.2010.01.006 |
| Reference:
|
[2] Bourdon, P. S., Noor, S. Waleed: Complex symmetry of invertible composition operators.J. Math. Anal. Appl. 429 (2015), 105-110. Zbl 1331.47039, MR 3339066, 10.1016/j.jmaa.2015.04.008 |
| Reference:
|
[3] Cowen, C. C., Ko, E.: Hermitian weighted composition operators on $H^2$.Trans. Am. Math. Soc. 362 (2010), 5771-5801. Zbl 1213.47034, MR 2661496, 10.1090/S0002-9947-2010-05043-3 |
| Reference:
|
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| Reference:
|
[5] Gao, Y. X., Zhou, Z. H.: Complex symmetric composition operators induced by linear fractional maps.Indiana Univ. Math. J. 69 (2020), 367-384. MR 4084175, 10.1512/iumj.2020.69.7622 |
| Reference:
|
[6] Garcia, S. R., Hammond, C.: Which weighted composition operators are complex symmetric?.Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation Operator Theory: Advances and Applications 236, Birkhäuser/Springer, Basel (2014), 171-179. Zbl 1343.47034, MR 3203059, 10.1007/978-3-0348-0648-0_10 |
| Reference:
|
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| Reference:
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[8] Garcia, S. R., Putinar, M.: Complex symmetric operators and applications II.Trans. Am. Math. Soc. 359 (2007), 3913-3931. Zbl 1123.47030, MR 2302518, 10.1090/S0002-9947-07-04213-4 |
| Reference:
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[9] Garcia, S. R., Wogen, W. R.: Complex symmetric partial isometries.J. Funct. Anal. 257 (2009), 1251-1260. Zbl 1166.47023, MR 2535469, 10.1016/j.jfa.2009.04.005 |
| Reference:
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[10] Garcia, S. R., Wogen, W. R.: Some new classes of complex symmetric operators.Trans. Am. Math. Soc. 362 (2010), 6065-6077. Zbl 1208.47036, MR 2661508, 10.1090/S0002-9947-2010-05068-8 |
| Reference:
|
[11] Jung, S., Kim, Y., Ko, E., Lee, J.: Complex symmetric weighted composition operators on $H^2(\mathbb{D})$.J. Funct. Anal. 267 (2014), 323-351. Zbl 1292.47014, MR 3210031, 10.1016/j.jfa.2014.04.004 |
| Reference:
|
[12] Matache, V.: Problems on weighted and unweighted composition operators.Complex Analysis and Dynamical Systems Trends in Mathematics, Birkhäuser, Cham (2018), 191-217. Zbl 07004622, MR 3784172, 10.1007/978-3-319-70154-7_11 |
| Reference:
|
[13] Narayan, S. K., Sievewright, D., Thompson, D.: Complex symmetric composition operators on $H^2$.J. Math. Anal. Appl. 443 (2016), 625-630. Zbl 1341.47030, MR 3508506, 10.1016/j.jmaa.2016.05.046 |
| Reference:
|
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| Reference:
|
[15] Noor, S. Waleed: Complex symmetry of composition operators induced by involutive ball automorphisms.Proc. Am. Math. Soc. 142 (2014), 3103-3107. Zbl 1302.47039, MR 3223366, 10.1090/S0002-9939-2014-12029-6 |
| Reference:
|
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| . |
