Achievement of continuity of $(ϕ,ψ)$-derivations without continuity
| dc.creator | Hejazian, S. | |
| dc.creator | Janfada, A. R. | |
| dc.creator | Mirzavaziri, M. | |
| dc.creator | Moslehian, M. S. | |
| dc.date | 2006-11-01 | |
| dc.date | 2007-01-21 | |
| dc.date.accessioned | 2026-07-07T07:41:56Z | |
| dc.date.available | 2026-07-07T07:41:56Z | |
| dc.description | Suppose that $\calak$ is a $C^*$-algebra acting on a Hilbert space $\calhk$, and that $ϕ, ψ$ are mappings from $\calak$ into $B(\calhk)$ which are not assumed to be necessarily linear or continuous. A $(ϕ, ψ)$-derivation is a linear mapping $d: \calak \to B(\calhk)$ such that $$d(ab)=ϕ(a)d(b)+d(a)ψ(b)\quad (a,b\in \calak).$$ We prove that if $ϕ$ is a multiplicative (not necessarily linear) $*$-mapping, then every $*$-$(ϕ,ϕ)$-derivation is automatically continuous. Using this fact, we show that every $*$-$(ϕ,ψ)$-derivation $d$ from $\calak$ into $B(\calhk)$ is continuous if and only if the $*$-mappings $ϕ$ and $ψ$ are left and right $d$-continuous, respectively. | |
| dc.description | To appear in Bull. Belgian Math Soc | |
| dc.identifier | https://arxiv.org/abs/math/0611016 | |
| dc.identifier | http://arxiv.org/abs/math/0611016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122300 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L57, 46L05, 47B47 | |
| dc.title | Achievement of continuity of $(ϕ,ψ)$-derivations without continuity | |
| dc.type | text |