BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bojan Kuzma (University of Primorska\, Slovenia) DTSTART:20240918T190000Z DTEND:20240918T200000Z DTSTAMP:20260420T053338Z UID:NYC-NCG/167 DESCRIPTION:Title: Birkhoff-James orthogonality in normed vector spaces\nby Bojan Kuzma (University of Primorska\, Slovenia) as part of Noncommutative geometry i n NYC\n\n\nAbstract\nBirkhoff-James orthogonality generalizes the classica l orthogonality from Hilbert to general normed spaces. It can be a useful tool for finding the best approximation of a vector within a given subspa ce. However\, unlike the classical one\, it is in general not symmetric. In fact (in dimensions greater than 2) it is symmetric if and only if the norm is induced by the inner product. This early classification of inner- product spaces goes back to James (for real Banach spaces) with an aid of Bohnenblust (for complex ones). One can visualize this relation as an inf inite directed graph (called ortho-digraph)\, where vertices are all the vectors from a normed space (or all points in its projectivisation) and tw o vertices x\, y form a directed edge if x is Birkhoff-James orthogonal t o y .We will show that this digraph contains a lot of information about th e normed space: It knows how to calculate the dimension of the underlying space\, knows if the norm is rotund or smooth\, knows how to find smooth p oints and in some special cases even knows if the underlying field is real or complex. At least for smooth spaces in can even completely characteriz e them\, modulo (conjugate) linear isometry.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/167/ END:VEVENT END:VCALENDAR