Displaying similar documents to “Lucid operators on Banach spaces”

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...

Ideals of finite rank operators, intersection properties of balls, and the approximation property

Åsvald Lima, Eve Oja (1999)

Studia Mathematica

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We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of c 0 , the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E). ...

Factoring Rosenthal operators.

Teresa Alvarez (1988)

Publicacions Matemàtiques

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In this paper we show that a Rosenthal operator factors through a Banach space containing no isomorphs of l.