Dunford–Schwartz theorem

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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.[1]

Statement

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The statement is no longer true when the boundedness condition is relaxed to even  .[2]

Notes

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  1. ^ Dunford, Nelson; Schwartz, J. T. (1956), "Convergence almost everywhere of operator averages", Journal of Rational Mechanics and Analysis, 5: 129–178, MR 0077090.
  2. ^ Friedman, N. (1966), "On the Dunford–Schwartz theorem", Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 5 (3): 226–231, doi:10.1007/BF00533059, MR 0220900, S2CID 122257150.