Question about Approximate spectrum of a bounded linear operator in a Hilbert space.

Question

We define the approximate spectrum of a bounded linear operator in a Hilbert space as
Let H be the Hilbert space over the field $K$
$\sigma_a(T)$={$\lambda \in K$ / $\exists$ $(x_n) \in H$ and $||x||=1$ and $(T-\lambda I)x_n \rightarrow 0$}
Can anyone give an example for this spectrum?

Answer 1

If $ \sigma(T)$ denotes the spectrum of $T$, then

$$ \partial \sigma(T) \subseteq \sigma_a(T).$$