Displaying similar documents to “On embedding l1 as a complemented subspace of Orlicz vector valued function spaces.”

On essentially incomparable Banach spaces.

Manuel González (1991)

Extracta Mathematicae

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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...

Sobczyk's theorems from A to B.

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

Extracta Mathematicae

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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 certain subsets of Bochner integrable function spaces.

Fernando Bombal (1991)

Extracta Mathematicae

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One of the most important methods used in literature to introduce new properties in a Banach space E, consists in establishing some non trivial relationships between different classes of subsets of E. For instance, E is reflexive, or has finite dimension, if and only if every bounded subset is weakly relatively compact or norm relatively compact, respectively. On the other hand, Banach spaces of the type C(K) and Lp(μ) play a vital role in the general...