Displaying similar documents to “On some subsets of L 1 ( μ , E ) ”

On certain subsets of Bochner integrable function spaces.

Fernando Bombal (1991)

Extracta Mathematicae

Similarity:

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...

An approach to Schreier's space.

Jesús M. Fernández Castillo, Manuel González (1991)

Extracta Mathematicae

Similarity:

In 1930, J. Schreier [10] introduced the notion of admissibility in order to show that the now called weak-Banach-Saks property does not hold in every Banach space. A variation of this idea produced the Schreier's space (see [1],[2]). This is the space obtained by completion of the space of finite sequences with respect to the following norm: ||x||S = sup(A admissible) ∑j ∈ A |xj|, ...

Some permanence results of properties of Banach spaces

Giovanni Emmanuele (2004)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Using some known lifting theorems we present three-space property type and permanence results; some of them seem to be new, whereas other are improvements of known facts.