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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 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. 


November 10, 2021
4:30 pm - 5:45 pm
Event Category:


Christina Edholm