## Projections on Banach spaces and a lifting property of operators (Prof. Botelho)

### November 10 @ 4:30 pm - 5:45 pm

**Title:** Projections on Banach spaces and a lifting property of operators

Prof. Maria Fernanda Botelho

Department of Mathematical Sciences

The University Of Memphis

**Abstract:** In this talk I will present properties of contractive projections and explain their role in the existence of norm preserving lifts of operators. A pair of Banach spaces *(X, J)*, with *J* a closed subspace of **X**, has the quotient lifting property (QLP) iff for every space **Y** and **S ∈ L(Y, X/J)**, there is **Ŝ** ** ∈ L(Y, X)**such that *S = π ◦ Ŝ*, where *π* denotes the quotient map from **X** onto **X/J**. This property was motivated by Lindenstrauss and Tzafriri lifting property for Banach spaces.

A pair of Banach spaces *(X,J)* has the QLP iff **J** is the kernel of a contractive projection on **X**. Several illustrative examples will be discussed.

**Bio-Sketch** for Fernanda Botelho:

I am a full professor in the Department of Mathematical Sciences at the University of Memphis. I earned a Doctor of Philosophy degree in Mathematics from the University of California at Berkeley and I did my undergraduate studies at the Universidade do Porto, Portugal.

My main research interest is in Operator Theory and Functional Analysis. I have authored and co-authored more than 80 research articles. I was a Donavant Professor in 2013-2016. I have been the coordinator for the Mathematical Sciences Graduate Programs since 2015.

I participated and organized several conferences, funded by the National Sciences Foundation and in collaboration with the Association for Women in Mathematics. I have served in programs geared to high school teachers and the professional training of graduate assistants.