A First Course In Functional Analysis 2

This text starts on an intermediate level of generality: sufficiently general to convey to the student the flavor of abstract methods in analysis and to cover many important applications, and still down-to-earth to make easy reading for beginners. The tradition founded by Banach, and favorable experiences from many courses, point to metric spaces as a suitable initial subject, and the present book keeps in this tradition ... The authors have selected and presented in a clear and readable way the basic material which is most likely to be used frequently. A wealth of examples, counterexamples, applications and exercises accompany the abstract theory throughout. --Mathematical Reviews

An attractive feature of the book is that each major theorem is followed by ... illustrations of its use. There are many well-chosen problems. Some problems ask the reader to apply an abstract idea to a concrete situation and others ask the reader to develop more theory. --American Mathematical Monthly