## Abstract We prove the Banach‐Steinhaus theorem for distributions on the space 𝒟(ℝ) within Bishop's constructive mathematics. To this end, we investigate the constructive sequential completion $ \tilde {\cal D} $(ℝ) of 𝒟(ℝ).
On the Banach-Steinhaus Theorem and the Continuity of Bilinear Mappings
✍ Scribed by Ronald Beattie; H.-P. Butzmann
- Publisher
- John Wiley and Sons
- Year
- 1991
- Tongue
- English
- Weight
- 929 KB
- Volume
- 153
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
In generalizing a result of Pełczynski the sequential weak to norm continuity of `Ž N-linear mappings between certain Banach spaces including spaces of type and . cotype will be studied. In particular, it is shown that every N-linear continuous n Ž . mapping from l l = иии = l l into l l is compact
Let X and Y be two real Hilbert spaces with the dimension of X greater than 1. Several cases about the Aleksandrov᎐Rassias problem for T : X ª Y preserving two or three distances are presented and geometric interpretations of these cases are also given.