Dunford–Pettis property

In functional analysis, the Dunford–Pettis property, named after Nelson Dunford and B. J. Pettis, is a property of a Banach space stating that all weakly compact operators from this space into another Banach space are completely continuous. Many standard Banach spaces have this property, most notably, the space C ( K ) {\displaystyle C(K)} of continuous functions on a compact space and the space L 1 ( μ ) {\displaystyle L^{1}(\mu )} of the Lebesgue integrable functions on a measure space.

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Dunford–Pettis property

In functional analysis, the Dunford–Pettis property, named after Nelson Dunford and B. J. Pettis, is a property of a Banach space stating that all weakly compact operators from this space into another Banach space are completely continuous. Many standard Banach spaces have this property, most notably, the space C ( K ) {\displaystyle C(K)} of continuous functions on a compact space and the space L 1 ( μ ) {\displaystyle L^{1}(\mu )} of the Lebesgue integrable functions on a measure space.

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Source: Wikipedia "Dunford–Pettis property" · CC BY-SA 4.0

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