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Volume 30, Issue 4
A Note on the Connectedness of the Invertible Group of a Nest Algebra

Min Zhang & Yue Hua

Commun. Math. Res., 30 (2014), pp. 329-333.

Published online: 2021-05

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  • Abstract

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.

  • Keywords

connectedness, nest algebra, invertible group.

  • AMS Subject Headings

47D25, 46K50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-30-329, author = {Min and Zhang and and 18872 and and Min Zhang and Yue and Hua and and 18873 and and Yue Hua}, title = {A Note on the Connectedness of the Invertible Group of a Nest Algebra}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {30}, number = {4}, pages = {329--333}, abstract = {

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} }
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 -

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.

Min Zhang & Hua Yue. (2021). A Note on the Connectedness of the Invertible Group of a Nest Algebra. Communications in Mathematical Research . 30 (4). 329-333. doi:10.13447/j.1674-5647.2014.04.06
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