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- W2950562769 abstract "Let ${mathcal N}$ and ${mathcal M}$ be nests on Banach spaces $X$ and $Y$ over the (real or complex) field $mathbb F$ and let $mbox{rm Alg}{mathcal N}$ and $mbox{rm Alg}{mathcal M}$ be the associated nest algebras, respectively. It is shown that a map $Phi:{rm Alg}{mathcal N}rightarrow{rm Alg}{mathcal M}$ is a Lie ring isomorphism (i.e., $Phi$ is additive, Lie multiplicative and bijective) if and only if $Phi$ has the form $Phi(A) = TAT^{-1} + h(A)I$ for all $Ain mbox{rm Alg}{mathcal N}$ or $Phi(A)=-TA^*T^{-1}+h(A)I$ for all $Ain mbox{rm Alg}{mathcal N}$, where $h$ is an additive functional vanishing on all commutators and $T$ is an invertible bounded linear or conjugate linear operator when $dim X=infty$; $T$ is a bijective $tau$-linear transformation for some field automorphism $tau$ of $mathbb F$ when $dim X<infty$." @default.
- W2950562769 created "2019-06-27" @default.
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- W2950562769 date "2013-01-31" @default.
- W2950562769 modified "2023-10-18" @default.
- W2950562769 title "Lie ring isomorphisms between nest algebras on Banach spaces" @default.
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- W2950562769 doi "https://doi.org/10.48550/arxiv.1301.7553" @default.
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