SOME CHARACTERIZATIONS OF FINITE-DIMENSIONAL HILBERT-SPACES

Authors
NAVARRO MA
Citation
Ma. Navarro, SOME CHARACTERIZATIONS OF FINITE-DIMENSIONAL HILBERT-SPACES, Journal of mathematical analysis and applications (Print), 223(1), 1998, pp. 364-365
Citations number
5
Categorie Soggetti
Mathematics,Mathematics,Mathematics,Mathematics
Journal title
Journal of mathematical analysis and applications (Print) → ACNP
ISSN journal
0022247X
Volume
223
Issue
1
Year of publication
1998
Pages
364 - 365
Database
ISI
SICI code
0022-247X(1998)223:1<364:SCOFH>2.0.ZU;2-F
Abstract
Let X be a finite-dimensional Banach space. The following affirmations are equivalent: 1. X is a Hilbert space. 2. Every extreme operator in X is an isometry. 3. The unit ball of L(X), the space of linear and c ontinuous operators in X, is the convex hull of its isometries. 4. The unit ball of L(X) is the closed convex hull of its isometries. (C) 19 98 Academic Press.