# Banach 22

This lecture ( banach22 ) was given on 10/16/09.

### Excerpt

Proved results addressing the following question.  $(e_j)_{j \in J}$ orthonormal set, and $(c_j)_{j \in J}$ a family of scalar, when does $\sum_J c_je_j$ converge?

Result: Every Hilbert space has an orthonomrla basis and any two o.n. bases have the same cardinality.