Answer to Question #139802 in Functional Analysis for anjali

Question #139802
Every Hilbert space has an orthonormal basis.
1
Expert's answer
2020-10-26T19:35:55-0400

The theorem states, that every Hilbert space contains a total orthonormal set. Furthermore, all total orthonormal sets in a Hilbert space H =/= {0} have the same cardinality, which is known as the Hilbert dimension. The proof requires the axiom of choice or Zorn’s lemma.

So, the statement is correct.


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