Definition 29.4.1 (Spectrum).label Let $A$ be a unital Banach algebra and $x \in A$, then
\[\sigma(x) = \sigma_{A}(x) = \bracs{\lambda \in \complex| \lambda - x \not\in G(A)}\]
is the spectrum of $x$ in $A$, and its complement is the resolvent set of $x$.
Post a Comment