Show that the linear span of a sequence (left(e_{n}ight)_{n in mathbb{N}} subset mathcal{H}, operatorname{span}left{e_{n}: e_{n} in mathcal{H},

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Show that the linear span of a sequence \(\left(e_{n}ight)_{n \in \mathbb{N}} \subset \mathcal{H}, \operatorname{span}\left\{e_{n}: e_{n} \in \mathcal{H}, n \in \mathbb{N}ight\}\), is a linear subspace of \(\mathcal{H}\).

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