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Isometric Reflections on Banach Spaces after a Paper of A. Skorik and M. Zaidenberg
- Source :
- Rocky Mountain J. Math. 30, no. 1 (2000), 63-83
- Publication Year :
- 2000
- Publisher :
- Rocky Mountain Mathematics Consortium, 2000.
-
Abstract
- Let E be a real Banach space. A norm-one element e in E is said to be an isometric reflection vector if there exist a maximal subspace M of E and a linear isometry F : E → E fixing the elements of M and satisfying F (e) = −e. We prove that each of the conditions (i) and (ii) below implies that E is a Hilbert space. (i) There exists a nonrare subset of the unit sphere of E consisting only of isometric reflection vectors, (ii) There is an isometric reflection vector in E, the norm of E is convex transitive, and the identity component of the group of all surjective linear isometries on E relative to the strong operator topology is not reduced to the identity operator on E.
Details
- ISSN :
- 00357596
- Volume :
- 30
- Database :
- OpenAIRE
- Journal :
- Rocky Mountain Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....edb4476bb2d95d4dacabb5c57d0ee80b