Isometries of absolute order unit spaces
| Autor: | Amit kumar, Anil Kumar Karn |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
021103 operations research General Mathematics 010102 general mathematics 0211 other engineering and technologies Order (ring theory) 02 engineering and technology Absolute value (algebra) Operator theory 01 natural sciences Functional Analysis (math.FA) Theoretical Computer Science Linear map Mathematics - Functional Analysis Matrix (mathematics) 46B40 (Primary) 46L05 46L30 (Secondary) FOS: Mathematics Isometry Bijection 0101 mathematics Unit (ring theory) Analysis Mathematics |
| Popis: | We prove that for a bijective, unital, linear map between absolute order unit spaces is an isometry if, and only if, it is absolute value preserving. We deduce that, on (unital) $JB$-algebras, such maps are precisely Jordan isomorphisms. Next, we introduce the notions of absolutely matrix ordered spaces and absolute matrix order unit spaces and prove that for a bijective, unital, linear map between absolute matrix order unit spaces is a complete isometry if, and only if, it is completely absolute value preserving. We obtain that on (unital) C$^*$-algebras such maps are precisely C$^*$-algebra isomorphism. 10 pages |
| Databáze: | OpenAIRE |
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