Spectral Theory of Compact Operators

The spectral theory of compact operators shows that these operators, though acting on infinite-dimensional spaces, share as much of their spectral behavior with ordinary matrices as any general operator can. It generalizes the Jordan canonical form of linear algebra: just as a matrix decomposes into invariant subspaces associated with its eigenvalues, a compact operator on a Banach or Hilbert space admits an analogous spectral decomposition, with the key difference that its eigenvalues can accumulate only at zero rather than occurring arbitrarily. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/