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Dirac functions, inner products and $T \in \mathcal{L}(G)$

If G is a countable group with neutral element e (and with the composition written multiplicatively). $\ell^2(G)$ consist of functions $x: G \to \mathbb{C} $ such that $\sum_{t \in G} \vert x(t) \vert^2 < \infty$ and with inner product \begin{equation} \langle x, y \rangle = \sum_{t \in G} x(t) \overline{y(t)} \end{equation} For $x,y \in \ell^2(G)$. […]

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Ask Mathematics

Dirac functions, inner products and $T \in \mathcal{L}(G)$

If G is a countable group with neutral element e (and with the composition written multiplicatively). $\ell^2(G)$ consist of functions $x: G \to \mathbb{C} $ such that $\sum_{t \in G} \vert x(t) \vert^2 < \infty$ and with inner product \begin{equation} \langle x, y \rangle = \sum_{t \in G} x(t) \overline{y(t)} \end{equation} For $x,y \in \ell^2(G)$. […]