Functional Analysis

This research group aims to advance our understanding of Lipschitz function spaces, Lipschitz-free spaces, and tensor products by developing and applying our existing knowledge of the extremal geometric structure of Banach spaces. Lipschitz functions are the most natural non-linear analog to continuous linear operators between Banach spaces. Every Lipschitz function between metric spaces admits a canonical linear extension between the corresponding Lipschitz-free spaces. Non-linear functional analysis is a comparatively new and active field of research with many unsolved internal problems, deep connections to related fields, and applications in discrete mathematics, optimal transport theory, graph theory, and computer science. Besides the scientific results, this project aims to produce PhDs for the needs of Estonia.

Research Group staff

Professor Rainis Haller (Head of Research Group)
Associate Professor Märt Põldvere
Research Fellow Johann Langemets
Research Fellow Aleksei Lissitsin
Research Fellow Katriin Pirk
Lecturer Kati Ain
Lecturer Natalia Saealle
Lecturer Indrek Zolk
PhD student Stefano Ciaci
PhD student Paavo Kuuseok
PhD student Julia Martsinkevitš
PhD student Tauri Viil
PhD student Andre Ostrak
Students: Jaan-Kristjan Kaasik, Tanel Kipper, Jaagup Kirme, Nikita Leo, Marcus Lõo, Triinu Veeorg

Topics:

diameter two properties and their dual properties;
geometric structure of Lipschitz function spaces and Lipschitz-free spaces;
existence and characterizations of Daugavet- and Delta-points;
the uniqueness of extensions in the Hahn-Banach theorem;
ball-covering properties;
plasticity of the unit ball.

Research Group projects

Current projects

PRG877 Extremal geometric structure of Banach spaces with applications to the study of Lipschitz function spaces, Lipschitz free spaces, and tensor products
PSG487 The big slice phenomena in Banach spaces with applications to the study of Lipschitz spaces

Main past projects

MOBTP138 Diameter two properties in Lipschitz spaces and in tensor products of Banach spaces (08.2019-12.2019)
PUTJD702 Geometry of the unit ball of a Banach space and the connections to diameter two properties (08.2018-07.2019)
IUT20-57 Structural Problems in Analysis, Algebra, and Geometry, with Applications to Numerical Analysis (01.2014-12.2019)

Relevant publications

Abrahamsen, Trond Arnold; Becerra Guerrero, Julio; Haller, Rainis; Lima, Vegard; Põldvere, Märt. (2021). Banach spaces where convex combinations of relatively weakly open subsets of the unit ball are relatively weakly open. Studia Mathematica [not yet published].
Haller, Rainis; Langemets, Johann; Lima, Vegard; Nadel, Rihhard; Rueda Zoca, Abraham (2020). On Daugavet indices of thickness. Journal of Functional Analysis.
Haller, Rainis; Pirk, Katriin; Veeorg, Triinu; (2020). Daugavet-and Delta-points in absolute sums of Banach spaces. Journal of Convex Analysis.
Oja, Eve; Saealle, Natalia; Zolk, Indrek (2020). Quantitative versions of almost squareness and diameter 2 properties. Acta et Commentationes Universitatis Tartuensis de Mathematica.
Ostrak, Andre (2020). Characterisation of the weak-star symmetric strong diameter 2 property in Lipschitz spaces. Journal of Mathematical Analysis and Applications.
Guirao, Antonio José; Lissitsin, Aleksei; Montesinos, Vicente (2019). Some remarks on the ball-covering property. Journal of Mathematical Analysis and Applications.
Langemets, Johann; López Pérez, Ginés (2019). Bidual octahedral renormings and strong regularity in Banach spaces. Journal of the Institute of Mathematics of Jussieu.
Haller, Rainis; Langemets, Johann; Põldvere, Märt (2015). On duality of diameter properties. Journal of Convex Analysis.

Recently defended doctoral dissertations

Rihhard Nadel, PhD, 2020. Supervisors: Rainis Haller, Vegard Lima, Johann Langemets. Big slices of the unit ball in Banach spaces. Institute of Mathematics and Statistics, Faculty of Science and Technology, University of Tartu, Estonia.
Katriin Pirk, PhD, 2020. Supervisiors: Rainis Haller, Johann Langemets, Trond Arnold Abrahamsen. Diametral diameter two properties, Daugavet-, and Delta-points in Banach spaces. Institute of Mathematics and Statistics, Faculty of Science and Technology, University of Tartu, Estonia.

Seminar on Functional Analysis
The seminar covers topics of interest of the Functional Analysis Research Group of the University of Tartu about the geometry of Banach spaces. During the seminars, the members of the research group, including students, present their latest research results. Invited (foreign) guests of the seminar will also speak to give us an overview of their research topics, to introduce their main results and ideas, and to share the current problems that have arisen and their attempts to solve them.