A set-theoretic approach to complete minimal systems in Banach spaces of bounded functions

Using independent families from combinatorial set theory, it is shown that for every infinite cardinal m, the dual of the space of all real-valued bounded functions on m contains a subspace which is isomorphic to a Hilbert space of dimension 2^m. This provides a new proof for the first step in the construction of complete minimal systems in Banach spaces of bounded functions.

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