An intuitive introduction to the construction of read-type operators

• Main Author: Xie, Mengyi
• Other Authors: Tang Wee Kee
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2021
• Subjects: Science::Mathematics
• Online Access: https://hdl.handle.net/10356/148531
• Institution: Nanyang Technological University

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.