Invariant Subspace Problem and Spectral Properties of Bounded Linear Operators on Banach Spaces, Banach Lattices, and Topological Vector Spaces

In Chapter 3 we use the results of Chapter 2 to prove locally-convex versions of some results on the Invariant Subspace Problem on Banach lattices obtained by Y. Abramovich, C Aliprantos, and O. Burkinshaw in 1993--98. For example, we show that if S and T are two commuting positive continuous operators with finite spectral radii on a locally convex-solid vector lattice, T is locally quasinilpotent at a positive vector, and S dominates a positive compact operator, then S and T have a common closed non-trivial invariant subspace.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Troitsky, Vladimir G.

Contributors dc:contributor

• Yuri Abramovich

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI9953162

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86988