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http://dx.doi.org/10.4134/JKMS.j190722

NORMAL COMPLEX SYMMETRIC WEIGHTED COMPOSITION OPERATORS ON THE HARDY SPACE  

Zhou, Hang (School of Science Department of Mathematics Tianjin Chengjian University)
Zhou, Ze-Hua (School of Mathematics Tianjin University)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.4, 2021 , pp. 799-817 More about this Journal
Abstract
In this paper, we investigate the normal and complex symmetric weighted composition operators W𝜓,𝜑 on the Hardy space H2(𝔻). Firstly, we give the explicit conditions of weighted composition operators to be normal and complex symmetric with respect to conjugations 𝒞1 and 𝒞2 on H2(𝔻), respectively. Moreover, we particularly investigate the weighted composition operators W𝜓,𝜑 on H2(𝔻) which are normal and complex symmetric with respect to conjugations 𝓙, 𝒞1 and 𝒞2, respectively, when 𝜑 has an interior fixed point, 𝜑 is of hyperbolic type or parabolic type.
Keywords
Normality; complex symmetric; weighted composition operators; automorphism; Hardy space;
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1 P. S. Bourdon and S. K. Narayan, Normal weighted composition operators on the Hardy space H2(𝕌), J. Math. Anal. Appl. 367 (2010), no. 1, 278-286. https://doi.org/10.1016/j.jmaa.2010.01.006   DOI
2 P. S. Bourdon and S. Waleed Noor, Complex symmetry of invertible composition operators, J. Math. Anal. Appl. 429 (2015), no. 1, 105-110. https://doi.org/10.1016/j.jmaa.2015.04.008   DOI
3 C. C. Cowen, Composition operators on H2, J. Operator Theory 9 (1983), no. 1, 77-106.
4 Y.-X. Gao and Z.-H. Zhou, Complex symmetric composition operators induced by linear fractional maps, Indiana Univ. Math. J. 69 (2020), no. 2, 367-384. https://doi.org/10.1512/iumj.2020.69.7622   DOI
5 S. R. Garcia and M. Putinar, Complex symmetric operators and applications. II, Trans. Amer. Math. Soc. 359 (2007), no. 8, 3913-3931. https://doi.org/10.1090/S0002-9947-07-04213-4   DOI
6 X. Hu, Z. Yang, and Z. Zhou, Complex symmetric weighted composition operators on Dirichlet spaces and Hardy spaces in the unit ball, Internat. J. Math. 31 (2020), no. 1, 2050006, 21 pp. https://doi.org/10.1142/S0129167X20500068   DOI
7 C. Jiang, X. Dong, and Z. Zhou, Complex symmetric Toeplitz operators on the unit polydisk and the unit ball, Acta Math. Sci. Ser. B (Engl. Ed.) 40 (2020), no. 1, 35-44. https://doi.org/10.1007/s10473-020-0103-2   DOI
8 T. Le, Self-adjoint, unitary, and normal weighted composition operators in several variables, J. Math. Anal. Appl. 395 (2012), no. 2, 596-607. https://doi.org/10.1016/j.jmaa.2012.05.065   DOI
9 S. Waleed Noor, Complex symmetry of composition operators induced by involutive ball automorphisms, Proc. Amer. Math. Soc. 142 (2014), no. 9, 3103-3107. https://doi.org/10.1090/S0002-9939-2014-12029-6   DOI
10 C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995.
11 S. R. Garcia, The eigenstructure of complex symmetric operators, in Recent advances in matrix and operator theory, 169-183, Oper. Theory Adv. Appl., 179, Birkhauser, Basel, 2008. https://doi.org/10.1007/978-3-7643-8539-2_10
12 S. R. Garcia and W. R. Wogen, Some new classes of complex symmetric operators, Trans. Amer. Math. Soc. 362 (2010), no. 11, 6065-6077. https://doi.org/10.1090/S0002-9947-2010-05068-8   DOI
13 S. K. Narayan, D. Sievewright, and D. Thompson, Complex symmetric composition operators on H2, J. Math. Anal. Appl. 443 (2016), no. 1, 625-630. https://doi.org/10.1016/j.jmaa.2016.05.046   DOI
14 C. Jiang, S.-A. Han, and Z. Zhou, Complex symmetric weighted composition operators on the Hardy space, Czechoslovak Math. J. 70(145) (2020), no. 3, 817-831. https://doi.org/10.21136/CMJ.2020.0555-18   DOI
15 S. Jung, Y. Kim, E. Ko, and J. E. Lee, Complex symmetric weighted composition operators on H2(𝔻), J. Funct. Anal. 267 (2014), no. 2, 323-351. https://doi.org/10.1016/j.jfa.2014.04.004   DOI
16 R. Lim and L. H. Khoi, Complex symmetric weighted composition operators on 𝓗γ(𝔻), J. Math. Anal. Appl. 464 (2018), no. 1, 101-118. https://doi.org/10.1016/j.jmaa.2018.03.071   DOI
17 S. Waleed Noor, On an example of a complex symmetric composition operator on H2(𝔻), J. Funct. Anal. 269 (2015), no. 6, 1899-1901. https://doi.org/10.1016/j.jfa.2015.06.019   DOI
18 X. Wang and Z. Gao, A note on Aluthge transforms of complex symmetric operators and applications, Integral Equations Operator Theory 65 (2009), no. 4, 573-580. https://doi.org/10.1007/s00020-009-1719-5   DOI
19 S. R. Garcia and M. Putinar, Complex symmetric operators and applications, Trans. Amer. Math. Soc. 358 (2006), no. 3, 1285-1315. https://doi.org/10.1090/S0002-9947-05-03742-6   DOI