6533b862fe1ef96bd12c613e
RESEARCH PRODUCT
On a theorem of Sobczyk
Aníbal Moltósubject
Pure mathematicsCompact spaceApproximation propertyGeneral MathematicsMathematical analysisEberlein–Šmulian theoremBanach spaceIsometryBanach manifoldHomeomorphismTopology (chemistry)Mathematicsdescription
In this paper the result of Sobczyk about complemented copies of c0 is extended to a class of Banach spaces X such that the unit ball of their dual endowed with the weak* topology has a certain topological property satisfied by every Corson-compact space. By means of a simple example it is shown that if Corson-compact is replaced by Rosenthal-compact, this extension does not hold. This example gives an easy proof of a result of Phillips and an easy solution to a question of Sobczyk about the existence of a Banach space E, c0 ⊂ E ⊂ l∞, such that E is not complemented in l∞ and c0 is not complemented in E. Assuming the continuum hypothesis, it is proved that there exists a Rosenthal-compact space K such that C(K) has no projectional resolution of the identity.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1991-02-01 | Bulletin of the Australian Mathematical Society |