Operators in Euclidean Spaces: Eight Selected Problems

Abstract

Generally speaking, an openator is a mapping from a topological vector space into itself. Thus, one of the main features in the theory of operators is the simultaneous availability of topological and vectorial structures. Euclidean spaces provide a prominent class of topological vector spaces, where the theory of operators becomes specially fruitful since in this case we have a vector space with a finite dimension, and a topological structure linked to the notion of inner product.