TY - JOUR
T1 - A Note on the Connectedness of the Invertible Group of a Nest Algebra
AU - Zhang , Min
AU - Hua , Yue
JO - Communications in Mathematical Research 
VL - 4
SP - 329
EP - 333
PY - 2021
DA - 2021/05
SN - 30
DO - http://doi.org/10.13447/j.1674-5647.2014.04.06
UR - https://global-sci.org/intro/article_detail/cmr/18954.html
KW - connectedness, nest algebra, invertible group.
AB - <p style="text-align: justify;">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.</p>