Resolvent set

In linear algebra and operator theory, the resolvent set of a linear operator is a set of complex numbers for which the operator is in some sense "well-behaved".be a linear operator with domainLet id denote the identity operator on X.is said to be a regular value if the following three statements are true: The resolvent set of L is the set of all regular values of L: The spectrum is the complement of the resolvent set and subject to a mutually singular spectral decomposition into the point spectrum (when condition 1 fails), the continuous spectrum (when condition 2 fails) and the residual spectrum (when condition 3 fails)., and condition 3 may be replaced by requiring that
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