Textbook in PDF format

'Functional Analysis Revisited' is not a first course in functional analysis – although it covers the basic notions of functional analysis, it assumes the reader is somewhat acquainted with them. It is by no means a second course either: there are too many deep subjects that are not within scope here. Instead, having the basics under his belt, the author takes the time to carefully think through their fundamental consequences. In particular, the focus is on the notion of completeness and its implications, yet without venturing too far from areas where the description 'elementary' is still valid. The author also looks at some applications, perhaps just outside the core of functional analysis, that are not completely trivial. The aim is to show how functional analysis influences and is influenced by other branches of contemporary mathematics. This is what we mean by 'Functional Analysis Revisited.'
Helps the reader gain a deeper understanding of functional analysis and its applications with accessible step-by-step explanations and examples
Demonstrates how the fundamental notion of completeness permeates contemporary mathematics
Reinforces learning with short chapter summaries and a variety of thoughtfully designed standard and nonstandard exercises