Abstract. In this note we return to some problems of general orthogonal series examined most intensively at the fifties. We show that the monotonicity conditions in four fundamental theorems of K. Tandori can be replaced by weaker assumptions.

AMS Subject Classification (1991): 40A30, 40G05

Keyword(s): orthogonal series, convergence, summability

Received March 2, 2010. (Registered under 16/2010.)