An intuitive introduction to the construction of read-type operators

The invariant subspace problem is an important yet partially resolved problem in the field of functional analysis. Since its first statement in the mid-1990s by von Neumann and Beurling, many mathematicians have attempted the problem and some variants of the problem have been solved by restricting t...

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Bibliographic Details
Main Author: Xie, Mengyi
Other Authors: Tang Wee Kee
Format: Final Year Project
Language:English
Published: Nanyang Technological University 2021
Subjects:
Online Access:https://hdl.handle.net/10356/148531
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Institution: Nanyang Technological University
Language: English
Description
Summary:The invariant subspace problem is an important yet partially resolved problem in the field of functional analysis. Since its first statement in the mid-1990s by von Neumann and Beurling, many mathematicians have attempted the problem and some variants of the problem have been solved by restricting the problem to particular classes of Banach spaces. The first example used to prove the neg- ative invariant subspace problem on a ”classical” Banach space was constructed by C.J.Read in 1984 where he provided a very sophisticated construction for operators with desired properties. In this thesis, we want to give an intuitive introduction to his construction in a more ”algorithmic” manner. By the end of this thesis, the reader should know how Read-type operators are constructed and why this class of operators prove the negative invariant subspace problem on l1 spaces.