Invariant Subspace Problem and Spectral Properties of Bounded Linear Operators on Banach Spaces, Banach Lattices, and Topological Vector Spaces
Troitsky, Vladimir G.
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https://hdl.handle.net/2142/86988
Description
Title
Invariant Subspace Problem and Spectral Properties of Bounded Linear Operators on Banach Spaces, Banach Lattices, and Topological Vector Spaces
Author(s)
Troitsky, Vladimir G.
Issue Date
1999
Doctoral Committee Chair(s)
Yuri Abramovich
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
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.
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