Context

Functional analysis

• 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?

Contents

• Idea
• Properties
• Related entries
• References

Idea

(…)

Properties

• relation to Calkin algebra: cf. Müller 2003 p. 167

spectrum of an operator

Calkin algebra

References

• Vladimir Müller: Essential Spectrum, Chapter III In: Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras, Operator Theory: Advances and Applications 139, Birkhäuser (2003) [doi:10.1007/978-3-0348-7788-6_3]

See also:

• Wikipedia: Essential spectrum

Created on November 4, 2025 at 10:17:33. See the history of this page for a list of all contributions to it.