Binormal and complex symmetric weighted composition operators on the Fock Space over $\mathbb{C}$

C. Santhoshkumar

doi:10.30970/ms.59.1.106-112

C. Santhoshkumar Corporate and Industry Relation, Amrita Vishwa Vidyapeetham Coimbatore, Tamilnadu, India

DOI: https://doi.org/10.30970/ms.59.1.106-112

Keywords: composition operators; weighted composition operators; Fock space; binormal; complex symmetry

Abstract

In this paper, we give simple characterization of binormal weighted composition operators $C_{\psi, \phi}$ on the Fock space over $\mathbb{C}$ where weight function is of the form $\psi(\zeta) = e^{\langle \zeta, c \rangle}$ for some $c \in \mathbb{C}$ . We derive conditions for $C_{\phi}$ to be binormal such that $C^*_{\phi}C_{\phi}$ and $C^*_{\phi} + C_{\phi}$ commute. Finally we give some simple characterization of binormal weighted composition operator to be complex symmetric.

Author Biography

C. Santhoshkumar, Corporate and Industry Relation, Amrita Vishwa Vidyapeetham Coimbatore, Tamilnadu, India

Corporate and Industry Relation, Amrita Vishwa Vidyapeetham

Coimbatore, Tamilnadu, India

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Binormal and complex symmetric weighted composition operators on the Fock Space over C\mathbb{C}

Abstract

Author Biography

References

Binormal and complex symmetric weighted composition operators on the Fock Space over $\mathbb{C}$