topological vector spaces

locally convex topological vector spaces

topological vector space

locally convex topological vector space

Banach 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

Stone-Weierstrass theorem

spectral theory

spectral theorem

Gelfand duality

functional calculus

Riesz representation theorem

measure theory

Bases

Algebraic Theories in Functional Analysis

An Elementary Treatment of Hilbert Spaces

When are two Banach spaces isomorphic?

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A Dirac distribution or Dirac $\delta$-distribution is a distribution that is given by evaluating a function at a point.