In mathematics, particularly functional analysis, the DunfordâÂÂSchwartz theorem, named after Nelson Dunford and Jacob T. Schwartz, states that the averages of powers of certain norm-bounded operators on L<sup>1</sup> converge in a suitable sense.
Let be a linear operator from to with and . Then
exists almost everywhere for all .
The statement is no longer true when the boundedness condition is relaxed to even .