In this paper, we study a practical way to obtain conjugations on the Hardy space H² via orthonormal basis. As a consequence, we get known examples and a new example of a conjugation family on H².

conjugations, Hardy space, complex symmetric operator, Toeplitz operator.

Received: February 17, 2022; Accepted: March 29, 2022; Published: April 5, 2022

How to cite this article: Marcos S. Ferreira and Geraldo De A. Júnior, Special conjugations on the Hardy space, International Journal of Functional Analysis, Operator Theory and Applications 14 (2022), 19-24. http://dx.doi.org/10.17654/0975291922003

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] Y.-B. Chung, Classification of Toeplitz operators on Hardy spaces of bounded domains in the plane, Math. Notes 101(3) (2017), 529-541.
[2] M. S. Ferreira, Some notes on complex symmetric operators, e-Journal of Analysis and Applied Mathematics 2021 (2021), 90-96.
[3] S. R. Garcia and M. Putinar, Complex symmetric operators and applications, Trans. Amer. Math. Soc. 358 (2006), 1285-1315.
[4] S. R. Garcia and M. Putinar, Complex symmetric operators and applications II, Trans. Amer. Math. Soc. 359 (2007), 3913-3931.
[5] S. R. Garcia and W. R. Wogen, Complex symmetric partial isometries, J. Funct. Anal. 257 (2009) 1251-1260.
[6] S. R. Garcia and W. R. Wogen, Some new classes of complex symmetric operators, Trans. Amer. Math. Soc. 362 (2010), 6065-6077.
[7] S. R. Garcia, E. Prodan and M. Putinar, Mathematical and physical aspects of complex symmetric operators, J. Phys. A 47 (2014), 1-51.
[8] E. Ko and J. E. Lee, On complex symmetric Toeplitz operators, J. Math. Anal. Appl. 434 (2016), 20-34.
[9] R. Li, Y. Yan and Y. Lu, A class of complex symmetric Toeplitz operators on Hardy and Bergman spaces, J. Math. Anal. 489 (2020), 1-12.