The Waring problem for noncommutative algebras

Date: June 15th, 2023
Time: 10:00
Place: Seminar 1 at IMAG building

Prof. Matej Bresar (Universities of Ljubljana and Maribor, Slovenia)

Abstract: Let 𝐴 be an algebra and let 𝑓=𝑓(𝑋1,…,𝑋𝑛) be a noncommutative polynomial. Set 𝑓(𝐴)={𝑓(𝑎1,…,𝑎𝑛):𝑎1,…𝑎𝑛∈𝐴}. The Waring problem for 𝐴 is to find a positive integer 𝑁 such that, for any 𝑓, every element in 𝑠𝑝𝑎𝑛𝑓(𝐴) can be written as a linear combination of 𝑁 elements from 𝑓(𝐴). We will discuss it for different matrix algebras.

Functional analisys seminar.