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Linear Maps Preserving Idempotence on Nest Algebras

✍ Scribed by Jian Lian Cui; Jin Chuan Hou

Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
2004
Tongue
English
Weight
230 KB
Volume
20
Category
Article
ISSN
1439-7617

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In this paper, we characterize rank-1 preserving linear maps between nest algebras acting on real or complex Banach spaces. As applications, we show that every weakly continuous and surjective local automorphism (or, anti-automorphism) on a nest algebra with an additional property is either an autom

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Let R be a commutative principal ideal domain, T : Mn(R) --\* Mm(R) an R-linear map which preserves idempotence. We determine the forms of T when n >/m and R ~ Fz, and solve some of Beasley's open problems. As a consequence, we prove that the set -~(R) of all R-linear maps on Mn(R) which preserve bo