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About: Decomposition of spectrum (functional analysis)     Permalink

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The spectrum of a linear operator that operates on a Banach space (a fundamental concept of functional analysis) consists of all scalars such that the operator does not have a bounded inverse on . The spectrum has a standard decomposition into three parts: * a point spectrum, consisting of the eigenvalues of ; * a continuous spectrum, consisting of the scalars that are not eigenvalues but make the range of a proper dense subset of the space; * a residual spectrum, consisting of all other scalars in the spectrum.

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