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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Norms of positive operators on $ L\sp p$-spaces

Authors: Ralph Howard and Anton R. Schep
Journal: Proc. Amer. Math. Soc. 109 (1990), 135-146
MSC: Primary 47B38; Secondary 47A30
MathSciNet review: 1000156
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Abstract: Let $ 0 \leq T:{L^p}(Y,\nu ) \to {L^q}(X,\mu )$ be a positive linear operator and let $ \vert\vert T\vert{\vert _{p,q}}$ denote its operator norm. In this paper a method is given to compute $ \vert\vert T\vert{\vert _{p,q}}$ exactly or to bound $ \vert\vert T\vert{\vert _{p,q}}$ from above. As an application the exact norm $ \vert\vert V\vert{\vert _{p,q}}$ of the Volterra operator $ Vf(x) = \int_0^x {f(t)dt} $ is computed.

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PII: S 0002-9939(1990)1000156-X
Keywords: Operator norms, positive linear operator, Volterra operator
Article copyright: © Copyright 1990 American Mathematical Society

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