A question from Conway's operator theory textbook, chapter 19 says
Fix an orthonormal basis $\mathcal{E}$ for $\mathcal{H}$ and define $\eta :c_0(\mathcal{E}) \rightarrow \mathcal{B}_0$ by $\eta(\{\alpha _e\})=\sum \alpha _e e\otimes e$.
Here, $\mathcal{H}$ is a Hilbert space.
What is the meaning of $c_0(\mathcal{E})$? Since the notation is missing from the textbook's index of symbols, I searched it online. I guess it means the set of sequences with terms from $\mathcal{E}$ that converge to $0$. But since the elemetns of $\mathcal{E}$ have unit norm, how can that sequence converge to $0$?
Any help is appreciated.