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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

Bounded Operators

Algebra of bounded operators, self-adjoint and unitary operators, spectral theorem in finite dimension.

Bounded operators Algebra B(H)Self-adjointness Unitary operators Normal operators Spectral theorem

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Lesson 5: Dirac Notation — Infinite Dimension

Lesson 7: Unbounded Operators