Fiber dimension for invariant subspaces

Li Chen, Guozheng Cheng, Xiang Fang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper we study the fiber dimension of invariant subspaces for a large class of operators. We define a class of invariant subspaces called CF subspaces which are related to the codimension-one property. We obtain several characterizations of CF subspaces, including one in terms of Samuel multiplicity.Other new findings include: (1) a lattice-additive formula and its applications (Section 4); (2) a new concept of "absorbance" which describes a rough containment relation for invariant subspaces (Section 5); (3) the existence of a unique, smallest CF subspace containing an arbitrary invariant subspace and preserving the fiber dimension (Section 6).

Original languageEnglish
Pages (from-to)2621-2646
Number of pages26
JournalJournal of Functional Analysis
Issue number9
StatePublished - 2015


  • Analytic operator
  • Fiber dimension
  • Invariant subspace
  • Samuel multiplicity


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