(untitled) (Communications in Mathematical Research, 2021)
The connectedness of the invertibles question for arbitrary nest has been reduced to the case of the lower triangular operators with respect to a fixed orthonormal basis e_n for n ≥ 1. For each f ∈ H^∞, let T_f be the Toeplitz operator. In this paper we prove that T_f can be connected to the identity through a path in the invertible group of the lower triangular operators if f satisfies certain conditions.