nLab essential spectrum

Definition

General

(…)

For self-adjoint operators

For self-adjoint operators the characterization simplifies: Their essential spectrum is the complement of the discrete spectrum (the latter being the discrete set of isolated eigenvalues with finite geometric multiplicity).

(cf. Moretti 2017 Rem. 9.15)

Properties

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

Related entries

• spectrum of an operator

• Calkin algebra

• Fredholm operator

References

• Martin Schechter: Fredholm Operators and the Essential Spectrum, New York University Courant Institute (1965) [pdf]

• 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]

• Valter Moretti: Spectral Theory and Quantum Mechanics, Springer (2017) [doi:10.1007/978-3-319-70706-8]

See also:

• Wikipedia: Essential spectrum