Dimension of Hilbert Space is Well-Defined
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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
- John B. Conway: A Course in Functional Analysis (1990)... (previous)... (next) $I.4.14$
