A Research on Some Decompositions Strategies of Function Algebras and Function Spaces: A Review

Exploring Decomposition Strategies in Function Algebras and Spaces

Abstract

“The only way to learn mathematics is to do mathematics.” Halmos is certainly not alone in this belief. The current set of notes is an activity-oriented companion to the study of linear functional analysis and operator algebras. It is intended as a pedagogical companion for the beginner, an introduction to some of the main ideas in this area of analysis, a compendium of problems I think are useful in learning the subject, and an annotated readingreference list. The great majority of the results in beginning functional analysis are straightforward and can be verified by the thoughtful student.