Essential spectrum

The essential spectrum or essential spectrum is an object from the mathematical branch of functional analysis. It is not uniformly defined in the literature. However, all definitions have in common that the essential spectrum is a subset of the spectrum of a linear operator, were at the points that are considered as " benign", removed.

Definition

One possible definition is: Be a linear operator on a Hilbert space, then there is a substantial range of from all of that is not a Fredholm operator. It is thus a generalization of the concept of intrinsic value.

Properties

The essential spectrum is invariant under disturbances with a compact operator It is therefore necessary.

For a normal operator on a Hilbert space if and only one of, if not an isolated eigenvalue of finite multiplicity is. Alternatively, the essential spectrum can be defined as the common spectrum of the image of the operator in Calkin algebra.