@article{Hu2025, 
author = {Xuke Hu and Yanyue Shi},
title = {Some Complex Symmetric Operators on Weighted Hardy Spaces},
year = {2025},
journal = {Periodical of Ocean University of China},
volume = {55},
number = {9},
pages = {158-164},
keywords = {weighted Hardy space, complex symmetric operators, Toeplitz operators, weighted composition operators},
url = {https://www.sciopen.com/article/10.16441/j.cnki.hdxb.20240117},
doi = {10.16441/j.cnki.hdxb.20240117},
abstract = {In this paper, we study the complex symmetry of weighted composite operators and Toeplitz operators on the weighted Hardy space H2(β) by constructing conjugate-linear involutions. When the weight coefficients are βn=bn, b≥1, we combine the operator J:    J  f  (  z  )  =            f      (                        z          ¯                    )        ¯   with the bounded weighted composite operator Wu, v to give Wu, vJ, and characterize when it is a conjugate-linear isometric involution. Furthermore, we obtain a necessary and sufficient condition for when the bounded weighted composite operator Wψ, φ, with respect to Wu, vJ, is complex symmetric. On the classical Hardy space, i.e. βn≡1, we use the idea of permutation method to construct an involutional linear isometric operator Cσ, and characterize the complex symmetry of Toeplitz operators and weighted composite operators with respect to Cσ.}
}