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New classes of spaces on which compact operators satisfy the Daugavet equation. (English) Zbl 0833.47023

New classes of spaces different from \(L_1 (\mu)\) and \(L_\infty (\mu)\) are presented, for which the Daugevet equation \[ |I+ T|= 1+ |T|\tag{DE} \] holds, where \(I\) the identity and \(T\) an arbitrary weakly compact operator. The last section of the paper can be viewed as a brief survey on the (DE) property.

MSC:

47B38 Linear operators on function spaces (general)
46B42 Banach lattices
47B07 Linear operators defined by compactness properties
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