Tags
Operators
Oct 15, 2021
Functional Analysis
68 min readFunctional Analysis (8): Spectral Theory — Decomposing Operators
The spectrum generalizes eigenvalues to infinite dimensions — the spectral theorem for bounded self-adjoint operators and continuous functional calculus give us a complete decomposition.
Oct 11, 2021
Functional Analysis
72 min readFunctional Analysis (6): Bounded Linear Operators and the Big Theorems
The Uniform Boundedness Principle, Open Mapping Theorem, and Closed Graph Theorem — three consequences of completeness that constrain how operators can behave.