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

## November 10, 2021 @ 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

**a closed subspace of**

*J**, has the quotient lifting property (QLP) iff for every space*

**X***and*

**Y***, there is*

**S ∈ L(Y, X/J)**

**Ŝ***such that*

**∈ L(Y, X)****, where**

*S = π ◦ Ŝ***denotes the quotient map from**

*π**onto*

**X***. This property was motivated by Lindenstrauss and Tzafriri lifting property for Banach spaces.*

**X/J**A pair of Banach spaces ** (X,J)** has the QLP iff

*is the kernel of a contractive projection on*

**J***. Several illustrative examples will be discussed.*

**X**

**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.