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Maximum average distance in complex finite dimensional normed spaces
- Source :
- Scopus-Elsevier
- Publication Year :
- 2002
- Publisher :
- Cambridge University Press (CUP), 2002.
-
Abstract
- A number r > 0 is called a rendezvous number for a metric space (M, d) if for any n ∈ ℕ and any x1,…xn ∈ M, there exists x ∈ M such that . A rendezvous number for a normed space X is a rendezvous number for its unit sphere. A surprising theorem due to O. Gross states that every finite dimensional normed space has one and only one average number, denoted by r (X). In a recent paper, A. Hinrichs solves a conjecture raised by R. Wolf. He proves that for any n-dimensional real normed space. In this paper, we prove the analogous inequality in the complex case for n ≥ 3.
Details
- ISSN :
- 17551633 and 00049727
- Volume :
- 66
- Database :
- OpenAIRE
- Journal :
- Bulletin of the Australian Mathematical Society
- Accession number :
- edsair.doi.dedup.....f1f1bcb8a43369cf6c723af74cbe18f1