[[Functional analysis MOC]]
# Spectrum

The **spectrum** $\sigma(T)$ of a [[Bounded operator|bounded]] or [[Unbounded operator|unbounded]] operator $T$ is the set of all $\lambda \in \mathbb{C}$ such that $T - \lambda \mathbf{I}$ has no [[Bounded operator|bounded]] and [[Densely defined operator|densely defined]] set-theoretic inverse. #m/def/anal/fun 
This is a generalization of [[Eigenvectors, eigenvalues, and eigenspaces|eigenvalues]].



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