Conjugations and Complex Symmetric Toeplitz Operators on the Weighted Hardy Space

Abstract

In this paper, we introduce a new conjugation Cξ on the weighted Hardy space Hρ(D) , where Cξ is given by (2.1) in Theorem 2.2. In particular, we prove that Cξ and Cμ,λ are unitarily equivalent where Cμ,λ is given in Ko and Lee (J Math Anal Appl 434:20–34, 2016). Using this, we investigate a complex symmetric Toeplitz operator Tφ with respect to the conjugation Cξ on the weighted Hardy space Hρ(D). Finally, we consider Cμ,λ-invariant of Berezin transform. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.