Displaying similar documents to “Total subspaces in dual Banach spaces which are not norming over any infinite-dimensional subspace”

Sobczyk's theorems from A to B.

Félix Cabello Sánchez, Jesús M. Fernández Castillo, David Yost (2000)

Extracta Mathematicae

Similarity:

Sobczyk's theorem is usually stated as: . Nevertheless, our understanding is not complete until we also recall: . Now the limits of the phenomenon are set: although c is complemented in separable superspaces, it is not necessarily complemented in a non-separable superspace, such as l.

On prequojections and their duals.

M. I. Ostrovskii (1998)

Revista Matemática Complutense

Similarity:

The paper is devoted to the class of Fréchet spaces which are called prequojections. This class appeared in a natural way in the structure theory of Fréchet spaces. The structure of prequojections was studied by G. Metafune and V. B. Moscatelli, who also gave a survey of the subject. Answering a question of these authors we show that their result on duals of prequojections cannot be generalized from the separable case to the case of spaces of arbitrary cardinality. We also introduce...

On essentially incomparable Banach spaces.

Manuel González (1991)

Extracta Mathematicae

Similarity:

We introduce the concept of essentially incomparable Banach spaces, and give some examples. Then, for two essentially incomparable Banach spaces X and Y, we prove that a complemented subspace of the product X x Y is isomorphic to the product of a complemented subspace of X and a complemented subspace of Y. If, additionally, X and Y are isomorphic to their respective hyperplanes, then the group of invertible operators in X x Y is not connected. The results can be applied to some classical...

Separable quotients of Banach spaces.

Jorge Mújica (1997)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

In this survey we show that the separable quotient problem for Banach spaces is equivalent to several other problems for Banach space theory. We give also several partial solutions to the problem.

Quotients of Banach Spaces with the Daugavet Property

Vladimir Kadets, Varvara Shepelska, Dirk Werner (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

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.