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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.
Doctoral Committee Chair(s):Yuri Abramovich
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
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.
Issue Date:1999
Type:Text
Language:English
Description:83 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999.
URI:http://hdl.handle.net/2142/86988
Other Identifier(s):(MiAaPQ)AAI9953162
Date Available in IDEALS:2015-09-28
Date Deposited:1999


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