Extreme points in spaces of operators and vector – valued measures
The geometry of -spaces over atomless measure spaces and the Daugavet property.
M-structure in tensor products of Banach spaces.
A proof of the Markov-Kakutani fixed point theorem via the Hahn-Banach theorem.
On the M-structure of the operator space L(CK)
Lipschitz spaces and M-ideals.
-ideals of compact operators into
We show for and subspaces of quotients of with a -unconditional finite-dimensional Schauder decomposition that is an -ideal in .
Structural properties of operator spaces
Property (M), M-ideals, and almost isometric structure of Banach spaces.
Remarks on rich subspaces of Banach spaces
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.
Quotients of Banach Spaces with the Daugavet Property
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.
Narrow operators and rich subspaces of Banach spaces with the Daugavet property
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).
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