Commun. Math. Res., 30 (2014), pp. 329-333.
Published online: 2021-05
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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 $n \geq 1$. 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.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2014.04.06}, url = {http://global-sci.org/intro/article_detail/cmr/18954.html} }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 $n \geq 1$. 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.