1: Hilbert Spaces. 2: Operators on Hilbert Space. 3: Banach Spaces. 4: Locally Convex Spaces. 5: Weak Topologies. 6: Linear Operators on a Banach Space. 7: Banach Algebras and Spectral Theory for Operators on a Banach Space. 8: C^* Algebras. 9: Normal Operators on Hilbert Space. 10: Unbounded Operators. 11: Fredholm Theory.
Corrected fourth printing
Second Edition J.B. Conway A Course in Functional Analysis "This book is an excellent text for a first graduate course in functional analysis ... Many interesting and important applications are included ... This book is a fine piece of work. It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author." -MATHEMATICAL REVIEWS