Arkiv för Matematik

  • Ark. Mat.
  • Volume 48, Number 2 (2010), 323-333.

Maximal invariant subspaces for a class of operators

Kunyu Guo, Wei He, and Shengzhao Hou

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Abstract

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 MTM<∞, 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 MzM<∞, 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.

Article information

Source
Ark. Mat., Volume 48, Number 2 (2010), 323-333.

Dates
Received: 23 September 2008
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907114

Digital Object Identifier
doi:10.1007/s11512-009-0109-1

Mathematical Reviews number (MathSciNet)
MR2672613

Zentralblatt MATH identifier
1198.47012

Rights
2009 © Institut Mittag-Leffler

Citation

Guo, Kunyu; He, Wei; Hou, Shengzhao. Maximal invariant subspaces for a class of operators. Ark. Mat. 48 (2010), no. 2, 323--333. doi:10.1007/s11512-009-0109-1. https://projecteuclid.org/euclid.afm/1485907114


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