A generalization of the cellular indecomposable property via fiber dimension

Guozheng Cheng, Xiang Fang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The cellular indecomposable property, introduced by Olin and Thomson in 1984 [11], is well known for the Dirichlet space, but it fails trivially for the vector-valued case. The purpose of this paper is to use the fiber dimension to reformulate the property such that it naturally extends the scalar-valued case, yet fix the vector-valued case in a meaningful way. Using the new formulation, we are able to generalize several previous results to the vector-valued setting. In particular, we extend a theorem of Bourdon relating the cellular indecomposable property and the codimension-one property to codimension- N. Several of our results appear to be new even for the Hardy space over the unit disc.

Original languageEnglish
Pages (from-to)2964-2985
Number of pages22
JournalJournal of Functional Analysis
Issue number10
StatePublished - 15 May 2011


  • Cellular indecomposable property
  • Codimension
  • Fiber dimension
  • Invariant subspace


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