Content deleted Content added
m Open access bot: url-access updated in citation with #oabot. |
mNo edit summary |
||
Line 1:
{{Short description|Spectral theory eigenvalue}}
In mathematics, specifically in [[spectral theory]], an [[eigenvalue]] of a [[Unbounded operator#Closed linear operators|closed linear operator]] is called '''normal''' if the space admits a decomposition into a direct sum of a finite-dimensional [[generalized eigenspace]] and an [[invariant subspace]] where <math>A-\lambda I</math> has a bounded inverse.
The set of normal eigenvalues coincides with the [[discrete spectrum (mathematics)|discrete spectrum]] <math>\sigma_d</math>.
==Root lineal==
Line 83:
The spectrum of a closed operator <math>A:\,\mathfrak{B}\to\mathfrak{B}</math> in the Banach space <math>\mathfrak{B}</math> can be decomposed into the union of two disjoint sets, the set of normal eigenvalues and the fifth type of the [[essential spectrum]]:
:<math>
\sigma(A)= \sigma_{\
</math>
| |||