Unconditional Convergence of General Fourier Series

We consider problems of unconditional convergence of Fourier series of functions with respect to general orthonormal systems (ONSs). Sufficient conditions on the functions of an ONS are found under which the Fourier series of every function with respect to this system converges unconditionally. We show that some of the obtained results are sharp. We also prove that from any ONS one can extract a subsequence with respect to which the Fourier series of every function converges unconditionally.