Identification of Polynomial Combinations of Operators

Presenter Information

Tova Lindberg, Minnesota State University, Mankato

Location

CSU 284A

Start Date

6-4-2010 10:00 AM

End Date

6-4-2010 12:00 PM

Student's Major

Mathematics and Statistics

Student's College

Science, Engineering and Technology

Mentor's Name

Namyong Lee

Mentor's Department

Mathematics and Statistics

Mentor's College

Science, Engineering and Technology

Description

In mathematical analysis, an important tool is the set of eigenvalues of an operator, which tells us something about the size of that operator. In algebra, addition and multiplication are actually important tools that help us understand how operators interact with each other. In this research project, we use these tools together in a new way to study combinations of operators. Using these tools, we take a particular combination of operators and see if we can work backwards through the combination to find out what the original operators were. This research project is focused on identifying which combinations will preserve the original operators so that we can tell exactly what those original operators were. The results of this project are then used by mathematical analysts in their study of abstract objects called algebras of bounded linear operators on Banach spaces.