The Generalized Toeplitz Determinants for a Class of Holomorphic Mappings in Several Complex Variables

In this paper, we define the generalized Toeplitz determinants whose entries are the coefficients of holomorphic functions on the unit disk \(\mathbb {U}\) $\mathbb{U}$ with k-fold symmetric, and then we establish the sharp bounds of the generalized determinants formed over the related terms of homogeneous expansion of a class of holomorphic mappings defined on the unit ball of a complex Banach space. The results presented here would generalize the corresponding results given by Giri and Kumar (Complex Anal Oper Theory 17(6):86, 2023).