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Hilbert Spaces and Linear Operators

Algebra & topology, linear operator theory & spectral theory. Dirac notation.

Lesson 1: Hilbert Spaces Lesson 2: Dual Space, Kets, Bras, Adjoint Lesson 3: Topology of Hilbert Spaces Lesson 4: Linear Operator Theory Lesson 5: Dirac Notation — Infinite Dimension Lesson 6: Bounded Operators Lesson 7: Unbounded Operators Lesson 8: Spectral Theory

Revision SheetsSheet 1: Dirac Reference Sheet Sheet 2: Atlas of Linear Operators

Spectral Theory

Spectrum and resolvent of self-adjoint operators, spectral measure, general spectral theorem, and functional calculus.

Spectrum Resolvent Spectral measure Spectral theorem Functional calculus Continuous spectrum Discrete spectrum

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Lesson 7: Unbounded Operators

Sheet 1: Dirac Reference Sheet