2-Local Derivations on Some $$ C^* $$ C ∗ -Algebras
| Autor: | Meysam Habibzadeh Fard, Abbas Sahleh |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Trace (linear algebra)
010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences Combinatorics Projection (relational algebra) symbols.namesake Von Neumann algebra symbols Pharmacology (medical) 0101 mathematics Algebra over a field Element (category theory) Unit (ring theory) Mathematics |
| Zdroj: | Bulletin of the Iranian Mathematical Society. 45:649-656 |
| ISSN: | 1735-8515 1017-060X |
| DOI: | 10.1007/s41980-018-0156-0 |
| Popis: | In this paper, we introduce the concept of trace-open projections in the second dual $$ \mathcal {A}^{**} $$ , of a $$ C^* $$ -algebra $$ \mathcal {A} $$ . This new concept is applied to show that if there is a faithful normal semi-finite trace $$ \tau $$ on $$ \mathcal {A}^{**} $$ such that $$ 1_{ \mathcal {A}^{**} } $$ is a $$ \tau $$ -open projection, then every 2-local derivation $$ \Delta $$ from $$ \mathcal {A} $$ to $$ \mathcal {A}^{**} $$ is an inner derivation. We also prove that the same conclusion holds for approximately 2-local derivations when $$ \mathcal {A}^{**} $$ is a finite von Neumann algebra without extra assumptions on its unit element. |
| Databáze: | OpenAIRE |
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