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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Analytic operator valued function space integrals as an $ {\scr L}(L\sb p,L\sb {p'})$ theory


Authors: Kun Soo Chang and Kun Sik Ryu
Journal: Trans. Amer. Math. Soc. 330 (1992), 697-709
MSC: Primary 46G12; Secondary 28C20, 47B38, 81S40
DOI: https://doi.org/10.1090/S0002-9947-1992-1038013-1
MathSciNet review: 1038013
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Abstract: The existence of an analytic operator-valued function space integral as an $ \mathcal{S}({L_p},{L_{p^{\prime}}})$ theory $ (1 \leq p \leq 2)$ has been established for certain functionals involving the Lebesgue measure. Recently, Johnson and Lapidus proved the existence of the integral as an operator on $ {L_2}$ for certain functionals involving any Borel measure. We establish the existence of the integral as an operator from $ {L_p}$ to $ {L_{p^{\prime}}}\;({1 < p < 2} )$ for certain functionals involving some Borel measures.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1038013-1
Keywords: Bochner integral, Feynman integral, Wiener integral, function space integral, Lebesgue decomposition, linear operator, strongly continuous, strongly measurable
Article copyright: © Copyright 1992 American Mathematical Society