In this talk, we will introduce the multi-Toeplitz operators on tensor Fock spaces. We completely characterize when the product of two multi-Toeplitz operators is also a multi-Toeplitz operator and when two multi-Toeplitz operators commute. As applications, some characterizations of the compactness, positivity, self-adjointness, normality, unitarity and isometry of multi-Toeplitz operators  are given here.

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