M-Structure and the space A(K,E)
For a compact convex set K and a Banach space E, under some natural M-structure theoretic conditions on K and E, we show that if the space of affine E-valued continuous functions on K is isometric to the space of E-valued continuous functions on some compact space, then K is a Bauer simplex. These r...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sapienza Università Editrice
1995-02-01
|
| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1995(1)/153-160.pdf |
| Summary: | For a compact convex set K and a Banach space E, under some natural M-structure theoretic conditions on K and E, we show that if the space of affine E-valued continuous functions on K is isometric to the space of E-valued continuous functions on some compact space, then K is a Bauer simplex. These results extend some well known characterizations of Bauer simplexes to the vector valued set up.
|
|---|---|
| ISSN: | 1120-7183 2532-3350 |