Datum in ura / Date and time: 8.11.21
(10:00 -- 11:00)
Predavalnica / Location: FAMNIT MP1
Predavatelj / Lecturer: Bojan Kuzma ( University of Primorska, Slovenia)
Naslov / Title: What does Birkhoff-James orthogonality know about the norm?
Vsebina / Abstract:
There are several possibilities to generalize the relation of orthogonality from Euclidean to arbitrary normed spaces. Among the better known is Birkhoff-James orthogonality, which is defined, in one of the equivalent ways, as $x \perp y$ if $y$ lies in the kernel of the supporting functional for $x$. This relation is homogeneous in both factors, but unlike Euclidean space it is not necessarily additive nor symmetric. We assign a (directed) graph to this relation with the nonzero vectors as the nodes and where each pair of orthogonal vectors forms a directed edge.
With the help of this graph one can show that Birkhoff-James orthogonality alone knows how to calculate the dimension of the underlying space, it knows whether the norm is smooth or not and whether it is strictly convex or not, and actually knows everything about the norm of smooth reflexive spaces up to (conjugate) linear isometry.
Among possible applications we mention the study of homomorphisms of the relation (i.e. not necessarily linear mappings that preserve orthogonality).
This is a joint work with Lj. Arambašić, A. Guterman, R. Rajić, and S. Zhilina
We are looking forward to meeting you at FAMNIT-MP1.
This Monday, November 8, 2021, from 10 am to 11 am.
Our Math Research Seminar will also be broadcasted via Zoom.
Join Zoom Meeting Here.
Everyone is welcome and encouraged to attend.