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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

Linear Operator Theory

Definition, domain, composition, continuity, and norm of linear operators in Hilbert space.

Linear operators Operator domain Operator composition Continuity Operator norm Adjoint Dense domain

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Lesson 3: Topology of Hilbert Spaces

Lesson 5: Dirac Notation — Infinite Dimension