Let f and g be functions, not identically zero, in the Fock space F-alpha(2) of C-n. We show that the product TfT(g) over bar of Toeplitz operators on F-alpha(2) is bounded if and only if f(z) = e(q(z)) and g(z) = ce(-q(z)), where c is a nonzero constant and q is a linear polynomial.
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