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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

2008

tom 56

nr 2

131-147

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.

Remarks on rich subspaces of Banach spaces

100%

Kadets V. , Kalton N. , Werner D.

tom 159

nr 2

195-206

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.

On the M-structure of the operator space L(CK)

75%

Werner D. , Werner W.

Studia Mathematica

1987

tom 87

nr 2

133-138