Integral operators in Banach spaces

Holub, J. R.

doi:10.1090/S0002-9939-1971-0293445-6

Integral operators in Banach spaces
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by J. R. Holub PDF

Proc. Amer. Math. Soc. 29 (1971), 75-80 Request permission

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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Séminaire Schwartz Année 1953/54

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