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.
DOI: http://dx.doi.org/10.7900/jot.2014jun22.2024
Keywords: fiber dimension, multiplier, complete Nevanlinna-Pick
kernel
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