A generalization of the cellular indecomposable property via fiber dimension

作者：Cheng Guozheng^*; Fang Xiang

来源：Journal of Functional Analysis, 2011, 260(10): 2964-2985.

DOI：10.1016/j.jfa.2011.02.009

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

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.

• 出版日期2011-5-15
• 单位温州大学