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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the structure of certain bounded linear operators


Author: G. D. Allen
Journal: Proc. Amer. Math. Soc. 53 (1975), 404-406
MSC: Primary 46E30; Secondary 60G99
MathSciNet review: 0438098
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Abstract: If every function $ f$ in the range of a bounded linear operator on $ {L_p}$ is equal to zero on a set of measure greater than a fixed number $ \epsilon $, it is shown that there is a common set of measure $ \epsilon $ on which every function is zero. A decomposition theorem for such operators is proved.


References [Enhancements On Off] (What's this?)

  • [1] Takeyuki Hida, Canonical representations of Gaussian processes and their applications., Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math. 33 (1960/1961), 109–155. MR 0119246

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DOI: https://doi.org/10.1090/S0002-9939-1975-0438098-2
Article copyright: © Copyright 1975 American Mathematical Society