Mathematics Ph.D. Dissertations
A Strictly Weakly Hypercyclic Operator with a Hypercyclic Subspace
Date of Award
2023
Document Type
Dissertation
Degree Name
Doctor of Philosophy (Ph.D.)
Department
Mathematics
First Advisor
Kit Chan (Committee Chair)
Second Advisor
Christopher Kluse (Other)
Third Advisor
Mihai Staic (Committee Member)
Fourth Advisor
Juan Bes (Committee Member)
Abstract
An interesting topic of study for a hypercyclic operator T on a topological vector space X has been whether X has an infinite-dimensional, closed subspaces consisting entirely, except for the zero vector, of hypercyclic vectors. These subspaces are called hypercyclic subspaces. The existence of a strictly weakly hypercyclic operator T, which is a weakly hypercyclic operator that is not norm hypercyclic on a Hilbert space H has been shown by Chan and Sanders. However, it is not known whether there exists a strictly weakly hypercyclic subspace of H. We first show that the left multiplication operator LT with the aforementioned strictly weakly hypercyclic operator T is a strictly WOT-hypercyclic operator on the operator algebra B(H). Then we obtain a sufficient condition for an operator T on a Hilbert space H to have a strictly weakly hypercyclic subspace. After that we construct an operator that satisfies these conditions and therefore prove the existence of a strictly weakly hypercyclic subspace.
Recommended Citation
Madarasz, Zeno, "A Strictly Weakly Hypercyclic Operator with a Hypercyclic Subspace" (2023). Mathematics Ph.D. Dissertations. 100.
https://scholarworks.bgsu.edu/math_diss/100