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Narrow operators and rich subspaces of Banach spaces with the Daugavet property

100%
Kadets V., Shvidkoy R., Werner D.
Studia Mathematica
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2001
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tom 147
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nr 3
269-298
EN
Let X be a Banach space. We introduce a formal approach which seems to be useful in the study of those properties of operators on X which depend only on the norms of the images of elements. This approach is applied to the Daugavet equation for norms of operators; in particular we develop a general theory of narrow operators and rich subspaces of spaces X with the Daugavet property previously studied in the context of the classical spaces C(K) and L₁(μ).
2
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Quotients of Banach Spaces with the Daugavet Property

100%
Kadets V., Shepelska V., Werner D.
Bulletin of the Polish Academy of Sciences. Mathematics
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2008
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tom 56
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nr 2
131-147
EN
We consider a general concept of Daugavet property with respect to a norming subspace. This concept covers both the usual Daugavet property and its weak* analogue. We introduce and study analogues of narrow operators and rich subspaces in this general setting and apply the results to show that a quotient of L₁[0,1] by an ℓ₁-subspace need not have the Daugavet property. The latter answers in the negative a question posed to us by A. Pełczyński.
3
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Remarks on rich subspaces of Banach spaces

100%
Kadets V., Kalton N., Werner D.
Studia Mathematica
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2003
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tom 159
|
nr 2
195-206
EN
We investigate rich subspaces of L₁ and deduce an interpolation property of Sidon sets. We also present examples of rich separable subspaces of nonseparable Banach spaces and we study the Daugavet property of tensor products.
4
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On the M-structure of the operator space L(CK)

74%
Werner D., Werner W.
Studia Mathematica
|
1987
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tom 87
|
nr 2
133-138
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