Year: 2024
Type: preprint
Abstract: Let $θ$ be a homomorphism on $L_0^\infty({\Bbb R}^+, ω)^*$. In this paper, we study left $θ$-derivations on $L_0^\infty({\Bbb R}^+, ω)^*$. We show that every left $θ$-derivation on $L_0^\infty({\Bbb R}^+, ω)^*$ is always a $θ$-derivation, and if $θ$ is isomorphism, then $L_0^\infty({\Bbb R}^+, ω)^*$ has no non-zero left $θ$-derivation. We also investigate automatic continuity, Singer-Wermer's conjecture and Posner's first theorem for left $θ-$derivations on $L_0^\infty({\Bbb R}^+, ω)^*$.
Source: arXiv (Cornell University)
Authors: Eisaei, M., Mehdipour, M. J., Moghimi, Gh. R.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4393212939