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Proceedings of the American Mathematical Society

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

 
 

 

Integral operators in Banach spaces


Author: J. R. Holub
Journal: Proc. Amer. Math. Soc. 29 (1971), 75-80
MSC: Primary 47B05; Secondary 47G05
DOI: https://doi.org/10.1090/S0002-9939-1971-0293445-6
MathSciNet review: 0293445
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Abstract: Giving a new proof of a result of Grothendieck, it is shown that a weak operator limit of a bounded net of integral maps is again integral and that every integral map is a weak operator limit of a net of finite dimensional maps which are uniformly bounded in nuclear norm. It is also shown that the subnuclear maps defined by Ruckle are precisely the integral maps. Using this result some questions of Ruckle are answered.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0293445-6
Keywords: Integral operator, subnuclear operator, nuclear operator, weak operator topology
Article copyright: © Copyright 1971 American Mathematical Society

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