Dear all,

The next Banach spaces webinar is on Friday May 29 9AM CDT (e.g., Dallas, TX time). Please join us at

https://unt.zoom.us/j/512907580

Speaker: Miguel Martin (University of Granada) Title: On Quasi norm attaining operators between Banach spaces

Abstract: This talk deals with a very recently introduced weakened notion of norm attainment for bounded linear operators. An operator $T\colon X \longrightarrow Y$ between the Banach spaces $X$ and $Y$ is quasi norm attaining if there is a sequence $(x_n)$ of norm one elements in $X$ such that $(Tx_n)$ converges to some $u\in Y$ with $|u|=|T|$. Norm attaining operators in the usual sense (i.e. operators for which there is a point in the unit ball where the norm of its image equals the norm of the operator) and compact operators satisfy this definition. The main result is that strong Radon-Nikodým operators (such as weakly compact operators can be approximated by quasi norm attaining operators (even by a stronger version of the definition), a result which does not hold for norm attaining operators. This allows us to give characterizations of the Radon-Nikodým property in term of the denseness of quasi norm attaining operators for both domain spaces and range spaces, extending previous results by Bourgain and Huff. We will also present positive and negative results on the denseness of quasi norm attaining operators, characterize both finite dimensionality and reflexivity in terms of quasi norm attaining operators, discuss conditions to obtain that quasi norm attaining operators are actually norm attaining, study the relationship with the norm attainment of the adjoint operator. We will finish the talk discussing some remarks and open questions.

The content of the talk is based on the recent preprint On Quasi norm attaining operators between Banach spaces by Geunsu Choi, Yun Sung Choi, Mingu Jung, and Miguel Martin.

* Please note that the new website for mathseminars.org is https://researchseminars.org/, which now lists seminars also from other sciences. (If you imported talk schedules to your calendar from mathseminars, you will have to delete and redo it from the new site.) * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach

Upcoming schedule

June 5: Denny Leung (National University of Singapore)

Thank you, and best regards,

Bunyamin Sari