In mathematics, or more specifically in spectral theory, the Riesz projector is the projector onto the eigenspace corresponding to a particular eigenvalue of an operator (or, more generally, a projector onto an invariant subspace corresponding to an isolated part of the spectrum).
It was introduced by Frigyes Riesz in 1912.
be a closed linear operator in the Banach space
be a simple or composite rectifiable contour, which encloses some region
and lies entirely within the resolvent set
Assuming that the contour
has a positive orientation with respect to the region
, the Riesz projector corresponding to
is the identity operator in
λ ∈ σ (
is the only point of the spectrum of
are invariant subspaces of the operator
are two different contours having the properties indicated above, and the regions
have no points in common, then the projectors corresponding to them are mutually orthogonal: