Isometries on L-2(X) and monotone functions
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We study necessary and sufficient conditions on a bounded operator T defined on the Hilbert space L-2(X) to be an isometry and show that, under suitable hypotheses, it suffices to restrict T to a smaller class of functions (e.g., if X = R+, to the cone of positive and decreasing functions). We also consider the problem of characterizing the sets Y subset of X for which the orthogonal projection of the operator T on L-2(Y) is also an isometry. Finally, we illustrate our results with several examples involving classical operators on different settings. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
CitationBoza, S.; Soria, J. Isometries on L-2(X) and monotone functions. "Mathematische Nachrichten", 01 Febrer 2014, vol. 287, núm. 2-3, p. 160-172.