Decomposition of spectrum (functional analysis)

The spectrum of a linear operator T {\displaystyle T} that operates on a Banach space X {\displaystyle X} is a fundamental concept of functional analysis. The spectrum consists of all scalars λ {\displaystyle \lambda } such that the operator T − λ {\displaystyle T-\lambda } does not have a bounded inverse on X {\displaystyle X} .