Al-Halees Hasan; Fleming Richard J.: Isomorphic vector-valued Banach-Stone theorems for subspaces. In: Acta scientiarum mathematicarum, (81) 1-2. pp. 189-214. (2015)
![[thumbnail of math_081_numb_001_002_189-214.pdf]](http://acta.bibl.u-szeged.hu/style/images/fileicons/part.png) |
Cikk, tanulmány, mű
math_081_numb_001_002_189-214.pdf Hozzáférés: Csak SZTE egyetemi hálózatról Letöltés (1MB) |
Absztrakt (kivonat)
Given a Banach space X, we define the number Ao(X) = inf d(X2,P(2)), where the infimum is taken over all two-dimensional subspaces X2 of X. Here, d(M, N) means the Banach-Mazur distance between Banach spaces M,N defined by d(M, N) = inf{||T||||T_1|| : T: M N is an isomorphism}. We establish some facts about Ao and then consider applications to Banach-Stone type theorems for isomorphisms on continuous, vector-valued function spaces. If Q,K are locally compact Hausdorff spaces, and X,Y are Banach spaces for which both Ao(X*) and AQ(Y*) are greater than one, it has been shown that if T is an isomorphism from CQ(Q. E) onto Co(K, Y) with ||T||||T~1 1| sufficiently small, then Q and K are homeomorphic, a generalization of the Banach-Stone Theorem for isometries. We examine such results for subspaces of these spaces. A closed subspace M of C'oiQ, X) is said to be a Co(Q)-module if it is closed under multiplication by functions in Co(<5). If M and N are Co(Q), Gb(X)-modules, respectively, then with assumptions similar to those mentioned above, we are able to obtain results in which the homeomorphism is between the strong boundaries of N and M. In this case, the strong boundaries are the subsets of K and Q, respectively, upon which the functions in N and M have nonzero values. We also obtain a new theorem concerning isometries.
| Mű típusa: | Cikk, tanulmány, mű |
|---|---|
| Befoglaló folyóirat/kiadvány címe: | Acta scientiarum mathematicarum |
| Dátum: | 2015 |
| Kötet: | 81 |
| Szám: | 1-2 |
| ISSN: | 0001-6969 |
| Oldalak: | pp. 189-214 |
| Nyelv: | angol |
| Kiadó: | Bolyai Institute, University of Szeged |
| Kiadás helye: | Szeged |
| Hivatalos webcím (URL): | http://www.acta.hu |
| Befoglaló mű URL: | http://acta.bibl.u-szeged.hu/38692/ |
| DOI: | 10.14232/actasm-014-255-x |
| Kulcsszavak: | Matematika |
| Megjegyzések: | Bibliogr.: p. 213-214. ; összefoglalás angol nyelven |
| Szakterület: | 01. Természettudományok 01. Természettudományok > 01.01. Matematika |
| Feltöltés dátuma: | 2016. okt. 17. 10:36 |
| Utolsó módosítás: | 2026. feb. 24. 11:13 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/35202 |
 |
Tétel nézet |
