Linear homeomorphisms of non-classical Hilbert spaces
| Autor: | W.H. Schikhof, H. Ochsenius |
|---|---|
| Rok vydání: | 1999 |
| Předmět: |
Unbounded operator
Discrete mathematics Mathematics(all) Pure mathematics General Mathematics Hilbert space Operator theory Compact operator on Hilbert space symbols.namesake Von Neumann's theorem symbols Open mapping theorem (functional analysis) Lp space Operator norm Mathematical Physics Mathematics |
| Zdroj: | Indagationes Mathematicae. New Series, 10, 4, pp. 601-613 Indagationes Mathematicae. New Series, 10, 601-613 |
| ISSN: | 0019-3577 |
| DOI: | 10.1016/s0019-3577(00)87912-4 |
| Popis: | Summary Let K be a complete infinite rank valued field. In [4] we studied Norm Hilbert Spaces (NHS) over K i.e. K-Banach spaces for which closed subspaces admit projections of norm ≤ 1. In this paper we prove the following striking properties of continuous linear operators on NHS. Surjective endomorphisms are bijective, no NHS is linearly homeomorphic to a proper subspace (Theorem 3.7), each operator can be approximated, uniformly on bounded sets, by finite rank operators (Theorem 3.8). These properties together — in real or complex theory shared only by finite-dimensional spaces — show that NHS are more ‘rigid’ than classical Hilbert spaces. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect