Theory of Linear Operators [Hardcover] [Jan 01, 2016] José A. Adell, A. Lekuona

The purpose of this book is to provide the basics regarding the mathematical key features of unbounded operators to readers that are not familiar with such technical aspects. In functional analysis and related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces. An operator between two normed spaces is a bounded linear operator if and only if it is a continuous linear operator. A continuous linear operator maps bounded sets into bounded sets. A linear functional is continuous if and only if its kernel is closed. Every linear function on a finite-dimensional space is continuous.