An 'analyst' is a mathematician who is seen habitually in the company of the real or complex numbers; a 'functional analyst' is an analyst who is not squeamish about using Zorn's lemma, definitely relishes the use of topology, and does not stand in the way of the internal algebraic impulses of the subject. The term 'functional analysis' dates from the early years of the subject, when abstract methods were novel and the principal motivation came from spaces whose elements are functions. Like other generic terms it is a catchall, encompassing a large part of the mathematical analysis of the last four decades. No portable textbook can hope to survey the subject.

Read more at http://ebookee.org/Lectures-in-Functional-Analysis-and-Operator-Theory_1515352.html#AQaCAhgryECsLiAW.99