Spectrum of an operator

Summary

The spectrum of a bounded operator $T$ on a complex Banach space is the set of complex numbers $\lambda$ for which $T - \lambda I$ is not invertible. It generalises the set of eigenvalues of a square matrix, the spectrum of a matrix. In infinite dimensions it can contain numbers that are not eigenvalues. It is always a nonempty compact subset of the plane when the space is not zero.