Test spaces, dacey spaces, and completeness of inner product spaces
Abstract
We show that a test space consisting of the unit sphere of a real or complex inner product space S and of the set all maximal orthonormal systems in S, is algebraic iff S is Dacey or, equivalently, iff S is complete. In addition, we present another completeness criterion.
- Publication:
-
Letters in Mathematical Physics
- Pub Date:
- December 1994
- DOI:
- 10.1007/BF00761140
- Bibcode:
- 1994LMaPh..32..299D
- Keywords:
-
- Primary: 46C15;
- Secondary: 81P10;
- 03G12