|
|||||
|
|
|
|
|
|
|
|
|
On Banach space valued
extensions from split faces
Tage Bai Andersen |
|
Vol. 42 (1972), No. 1, 1–9
|
Abstract |
|
The object of this note is the following theorem: Suppose a is a continuous affine map from a closed split face F of a compact convex set K with values in a Banach space B enjoying the approximation property. Suppose also that p is a strictly positive lower semi-continuous concave function on K such that ∥a(k)∥≦ p(k) for all k in F. Then a admits a continuous affine extension ã to K into B such that ∥ã(k)∥≦ p(k) for all k in K. |
Mathematical Subject Classification 2000
Primary: 46E15
Secondary: 46B99, 46A05
|
Milestones
Received: 30 March 1971
Published: 1 July 1972
|
Authors |
| Tage Bai Andersen | |
|
