A Study on Cubature Formulas and ISO Metric Embeddings: Exploring the properties of normed spaces and Euclidean subspaces

Abstract

The subject of the present work arose in a connection with well-known and deeply developed problem about almost Euclidean subspaces of normed spaces. This is far from being a complete list of the publications about the subject. As a rule, a normed space does not contain Euclidean subspaces of dimensions greater than one. However, the famous Dvoretzky theorem states the existence of almost Euclidean subspaces of all normed spaces of sufficiently big dimensions.