My Research Journey on Cesaro Averaging and New Invariant Banach Limits on L∞ and L∞(0,∞)


I will present joint work with my advisor Chris Lennard, and his former student Jeromy Sivek. While discussing the results we obtained, I will also talk about the different stages we went through during our research for this project. I will start on the sequence space l, where we constructed Banach limits that are invariant under the Cesàro Averaging operator. Next, I will discuss our results on the function space L(0,∞). Here we defined a new operator Jα , for α > 0. This new operator extends the definition of Jn , with n ∈ N, which is the operator obtained by composing the Cesàro Averaging operator with itself n times. We showed that the family of operators {Jα}α>0 has the semigroup property, and we also constructed Banach limits that are invariant under these operators. 

Monday, February 17, 2020 - 16:30

703 Thackeray Hall

Speaker Information
Pamela Delgado
University of Pittsburgh