Category:Hilbert Sequence Space

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This category contains results about Hilbert Sequence Space.

Let $d_2: A \times A: \to \R$ be the real-valued function defined as:

$\displaystyle \forall x = \left\langle{x_i}\right\rangle, y = \left\langle{y_i}\right\rangle \in A: d_2 \left({x, y}\right) := \left({\sum_{k \mathop \ge 0} \left({x_k - y_k}\right)^2}\right)^{\frac 1 2}$

The metric space $\left({A, d_2}\right)$ is the Hilbert sequence space on $\R$ and is denoted $\ell^2$.