The root note for Kreyszig’s Introductory Functional Analysis with Applications. These are a little bit outdated and unfortunately out of order; I will get to ordering these soon.
Adjoint Operators and Reflexivity
On Spectral Families of Hermitian Operators
A Nice Diagonalization Argument
Spectra of Bounded Operators in Banach Space
Spectral Theory of Compact Operators
Self-Adjoint Operator Properties
More recently I started reviewing Kreyszig again for a functional analysis course. Below are some additional notes I’ve written as I was revisiting the book.