Dimension of Hilbert Space is Well-Defined

Definition

Let $H$ be a Hilbert space.

Then the dimension $\dim H$ of $H$ is well-defined.

That is to say, any two bases of $H$ have the same cardinality.

Proof

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Sources

• 1990: John B. Conway: A Course in Functional Analysis (2nd ed.) ... (previous) ... (next) $I.4.14$