# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.333171

Arkiv for Matematik, 48, (2), 323-333, 2008.9
In this note, we characterize maximal invariant subspaces for a class of operators. Let$T$be a Fredholm operator and $1-TT^{*}\in\mathcal{S}_{p}$ for some$p$≥1. It is shown that if$M$is an invariant subspace for$T$such that dim$M$$⊖$$TM$<∞, then every maximal invariant subspace of$M$is of codimension 1 in$M$. As an immediate consequence, we obtain that if$M$is a shift invariant subspace of the Bergman space and dim$M$$⊖$$zM$<∞, then every maximal invariant subspace of$M$is of codimension 1 in$M$. We also apply the result to translation operators and their invariant subspaces.
@inproceedings{kunyu2008maximal,
title={Maximal invariant subspaces for a class of operators},
author={Kunyu Guo, Wei He, and Shengzhao Hou},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203627502384980},
booktitle={Arkiv for Matematik},
volume={48},
number={2},
pages={323-333},
year={2008},
}

Kunyu Guo, Wei He, and Shengzhao Hou. Maximal invariant subspaces for a class of operators. 2008. Vol. 48. In Arkiv for Matematik. pp.323-333. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203627502384980.