nLab functional analysis - contents

• Functional Analysis

Overview diagrams

• topological vector spaces

• locally convex topological vector spaces

Basic concepts

• topological vector space

  • locally convex topological vector space

  • Banach Spaces

    • reflexive

  • Smith Spaces

  • Hilbert Spaces, Fréchet Spaces, Sobolev spaces, Lebesgue Spaces

  • Bornological Vector Spaces

  • Barrelled Vector Spaces

• linear operator

  • bounded, unbounded, self-adjoint, compact, Fredholm

  • spectrum of an operator

• operator algebras

  • functional calculus

Theorems

• Stone-Weierstrass theorem

• spectral theory

  • spectral theorem

  • Gelfand duality

• functional calculus

• Riesz representation theorem

• measure theory

Topics in Functional Analysis

• Bases

• Algebraic Theories in Functional Analysis

• An Elementary Treatment of Hilbert Spaces

• When are two Banach spaces isomorphic?

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