Decomposition of spectrum (functional analysis)

The spectrum of a linear operator ${\displaystyle T}$ that operates on a Banach space ${\displaystyle X}$ (a fundamental concept of functional analysis) consists of all scalars ${\displaystyle \lambda }$ such that the operator ${\displaystyle T-\lambda }$ does not have a bounded inverse on ${\displaystyle X}$. The spectrum has a standard decomposition into three parts:

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