Acta mathematica scientia,Series A
• Articles • Next Articles
Cui Jianlian; Hou Jinchuan
Received:
Revised:
Online:
Published:
Contact:
Abstract: Let ${\cal N}$ and ${\cal M}$ be two nests on real or complex Banach spaces X and Y, respectively, and $\Phi$ be an additive map between ideals Alg$_{\cal F}{\cal N}$ and Alg$_{\cal F}{\cal M}$ of finite rank operators in nest algebras Alg${\cal N}$ and Alg${\cal M}$, of which the range contains all rank-1 nilpotent operators in Alg${\cal M}$. The authors show that if $\Phi$ is rank-1 nilpotency preserving in both directions, then $\Phi$ has the form either $\Phi(x\otimes f)=Ax\otimes Cf$ for every rank-1 nilpotent operator $x\otimes {\rm Alg}_{\cal F}{\cal N}$ or $\Phi(x\otimes f)=Af\otimes Cx$ for every rank-1 nilpotent operator $x\otimes f\in {\rm Alg}_{\cal F}{\cal N}$,where $A$ and $C$ are certain $\tau$-linear operators with an automorphism $\tau$ of the underlying field. And the authors obtain particularly a characterization of such $\Phi$ if it is continuous, $X$ and $Y$ are Hilbert spaces with dimX≥ 6.
Key words: Additive map, Rank one nilpotent operator, Nest algebra
CLC Number:
Cui Jianlian; Hou Jinchuan. Additive Maps Preserving Rank-1 Nilpotency on Nest Algebras[J].Acta mathematica scientia,Series A, 2007, 27(2): 193-203.
0 / / Recommend
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
URL: http://121.43.60.238/sxwlxbA/EN/
http://121.43.60.238/sxwlxbA/EN/Y2007/V27/I2/193
Cited