A generalization of the cellular indecomposable property via fiber dimension |
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Authors: | Guozheng Cheng Xiang Fang |
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Affiliation: | a School of Mathematics, Wenzhou University, Wenzhou, Zhejiang 325035, China b Department of Mathematics, Kansas State University, Manhattan, KS 66502, United States |
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Abstract: | 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. |
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Keywords: | Cellular indecomposable property Fiber dimension Codimension Invariant subspace |
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