Definition:Dimension (Hilbert Space)

This page is about Dimension in the context of Hilbert Space. For other uses, see Dimension.

Definition

Let $H$ be a Hilbert space, and let $E$ be a basis of $H$.

Then the dimension $\dim H$ of $H$ is defined as $\card E$, the cardinality of $E$.

Also see

• Dimension of Hilbert Space is Well-Defined, showing that $\dim H$ does not depend on the particular choice of $E$.

Sources

• 1990: John B. Conway: A Course in Functional Analysis (2nd ed.) ... (previous) ... (next) $I.4.15$