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.