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Randomly Weighted Series of Contractions in Hilbert Spaces

1996
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Mathematica Scandinavica
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Conditions are given for the convergence of randomly weighted series of contractions in Hilbert spaces. It is shown that under these conditions the series converges in operator norm outside of a (universal) null set simultaneously for all Hilbert spaces and all contractions of them. The conditions obtained are moreover shown to be as optimal as possible. The method of proof relies upon the spectral lemma for Hilbert space contractions (which allows us to imbed the initial problem into a setting

doi:10.7146/math.scand.a-12606
fatcat:mtkfyhyn7ncqbjoeupbvnehgne