Displaying similar documents to “Weak Grothendieck's theorem.”

Some problems on narrow operators on function spaces

Mikhail Popov, Evgenii Semenov, Diana Vatsek (2014)

Open Mathematics

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It is known that if a rearrangement invariant (r.i.) space E on [0, 1] has an unconditional basis then every linear bounded operator on E is a sum of two narrow operators. On the other hand, for the classical space E = L 1[0, 1] having no unconditional basis the sum of two narrow operators is a narrow operator. We show that a Köthe space on [0, 1] having “lots” of nonnarrow operators that are sum of two narrow operators need not have an unconditional basis. However, we do not know if...