Toeplitz Operators with Positive Operator-Valued Symbols on Vector-Valued Generalized Fock Spaces

In this article, we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces $$F_\varphi^2$$ . Main results including Fock-Carleson condition, bounded Toeplitz operators, compact Toeplitz operators, and Toeplitz operators in the Schatten-p class are all considered.