NEST代数的局部自同构

Local Automorphisms of Nest Algebras

本文研究自反Banach空间中nest代数上的局部自同构,并考察nest代数上自同构集合的代数自反性.证明了nest代数上强算子连续的满局部自同构是自同构,得到有限维空间上nest代数的自同构集合是代数自反的结论.

This paper is concerned with the local automorphisms of nest algebras on reflexive Banach spaces and the algebraic reflexivity of the sets of all automorphisms on these algebras. We show that all strongly continuous surjective local automorphisms of nest algebras are automorpisms. In particular, we obtain the result that the set of all automorphisms as the subset of all invertible linear transformations of nest algebra on finite dimensional space is alggebraically reflexive.