Definition:Square Summable Mapping

Definition

Let $\GF$ be a subfield of $\C$.

Let $I$ be a set.

Let $f: I \to \GF$ be a mapping.

Then $f$ is said to be square summable if and only if:

$\set{ i \in I: \map f i \ne 0 }$ is countable

$\ds \sum_{i \mathop \in I} \cmod{ \map f i }^2 < \infty$

Sources

• 1990: John B. Conway: A Course in Functional Analysis (2nd ed.) ... (previous) ... (next): $\text{I}$ Hilbert Spaces: $\S 1.$ Elementary Properties and Examples: Example $1.7$

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