Analysis Seminar: Restricted isometries and operator norms on finite-dimensional $L^p$-spaces (Alonso Delfín Ares de Parga, CU Boulder)
April 2 @ 4:15 pm - 5:15 pm
Abstract: An isometry between two normed vector spaces is a linear map that preserves the norm (i.e., the length of each output agrees with the length of its input). For the classical $p$-norms, isometries have a very concrete description when $p\neq 2$: they are given by signed permutations of the coordinates.
In this talk, I will present a generalization of this result to restricted isometries, which are linear maps that preserve the norm only on a fixed subset of coordinates. I will discuss how this generalization could be used in the computation of certain $p$-operator norms, a problem that is known to be NP-hard in general.
This talk includes joint work carried out as part of two REU projects in 2024 and 2025.