In this program
- Weak and weak-* topologies (introduction)
- Compact operators
- Fredholm theory (overview)
- Spectral theorem for bounded self-adjoint operators (introduction)
Functional analysis topics
Spectral theorem for bounded self-adjoint operators (introduction)
Graduate analysis · Theoretical / proof-based
Topic
Spectral theorem for bounded self-adjoint operators (introduction)
Graduate Analysis — scope drawn from Axler Measure, Integration & Real Analysis (open access), Bass Real Analysis for Graduate Students (free PDF), and typical first-year graduate analysis syllabi.