Spectral projections are linear operators that arise in the spectral decomposition of an operator, associated with the eigenvalues and corresponding eigenvectors. They allow us to isolate parts of an operator related to specific spectral values, playing a crucial role in understanding unbounded self-adjoint operators, functional calculus, and the spectrum of an operator. These projections help in analyzing how operators behave across different subspaces linked to their spectral properties.
congrats on reading the definition of spectral projections. now let's actually learn it.