In mathematics, particularly functional analysis, the Dunford–Schwartz theorem, named after Nelson Dunford and Jacob T. Schwartz states that the averages of powers of certain norm-bounded operators on L1 converge in a suitable sense.
Statement of the theorem
The statement is no longer true when the boundedness condition is relaxed to even .
- Dunford, Nelson; Schwartz, J. T. (1956), "Convergence almost everywhere of operator averages", Journal of Rational Mechanics and Analysis, 5: 129–178, MR 77090.
- Friedman, N. (1966), "On the Dunford–Schwartz theorem", Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 5 (3): 226–231, MR 220900, doi:10.1007/BF00533059.
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