By definition the Riesz projection of a Banach algebra element $a$ associated with a complex number $\alpha$ is given by $p(\alpha , a)= \frac{1}{2\pi i} \int_{\Gamma} ( \mu -a)^{-1} \,\, \text{d}\mu,$ where $\Gamma$ is a small curve isolating $\alpha$ from the rest of the spectrum of $a.$ Am able to apply this correctly in order to get the intended result. However, am facing a challenge to use this definition when $\alpha $ is replaced with a set $\partial B(\alpha_{i},\epsilon).$ Could someone please help me how the definition change when $\alpha $ is replaced with a set $\partial B(\alpha_{i},\epsilon).$ Thanks in advance.
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