The Resolvent Theorem states that for a bounded linear operator on a Banach space, the resolvent can be used to characterize the spectrum of that operator. This theorem connects the resolvent set, which consists of those complex numbers where the resolvent operator is defined, to the spectral properties of the operator. It plays a crucial role in understanding how operators behave and how their spectra can be analyzed through resolvents.
congrats on reading the definition of Resolvent Theorem. now let's actually learn it.