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Complex Interpolation of Compact Operators Mapping into Lattice Couples

Võrepaaridesse kujutavate kompaktsete operaatorite kompleksne interpolatsioon

並列摘要


After 44 years it is still not known whether an operator mapping one Banach couple boundedly into another and acting compactly on one (or even both) of the ”endpoint” spaces also acts compactly between the complex interpolation spaces generated by these couples. We answer this question affirmatively in certain cases where the ”range” Banach couple is a couple of lattices on the same measure space.

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