Böcker av Charles W (New Mexico State Univ Swartz

The book presents a theory of abstract duality pairs which arises by replacing the scalar field by an Abelian topological group in the theory of dual pair of vector spaces. Examples of abstract duality pairs are vector valued series, spaces of vector valued measures, spaces of vector valued integrable functions, spaces of linear operators and vector valued sequence spaces. These examples give rise to numerous applications such as abstract versions of the Orlicz-Pettis Theorem on subseries convergent series, the Uniform Boundedness Principle, the Banach-Steinhaus Theorem, the Nikodym Convergence theorems and the Vitali-Hahn-Saks Theorem from measure theory and the Hahn-Schur Theorem from summability. There are no books on the current market which cover the material in this book. Readers will find interesting functional analysis and the many applications to various topics in real analysis.

Presents a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil, and McShane. This book shows how fresh theories of integration were developed to solve problems that earlier theories could not handle. It develops the basic properties of each integral in detail and compares the different integrals.

A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators, such as a method for defining "functions of an operator". This book contains an exposition of several such functional calculi.

Presents an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis. This book explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces.