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Journal of Operator Theory

Volume 74, Issue 2, Fall 2015  pp. 319-328.

A uniform approach to fiber dimension of invariant subspaces

Authors:  Li Chen
Author institution: Department of Mathematics, Tianjin University, Tianjin, 300072, China

Summary:  We provide a unified approach to fiber dimension of invariant subspaces in vector-valued analytic function spaces. Based on an elementary observation on linear equations, it is shown that the fiber dimension is an additive invariant for multiplier invariant subspaces in case the function space admits a complete Nevanlinna--Pick kernel, and a similar approach applies to give new simple proofs of two important theorems on fiber dimension recently established relating respectively to the cellular indecomposable property and the transitive algebra problem.

Keywords:  fiber dimension, multiplier, complete Nevanlinna-Pick kernel

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