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Bimodules over nest algebras and Deddens' theorem 总被引:1,自引:0,他引:1
I. Todorov 《Proceedings of the American Mathematical Society》1999,127(6):1771-1780
We generalize Deddens' theorem for nest algebras in the case of w*-closed nest algebras bimodules. For each such bimodule, we introduce a norm closed sub-bimodule of it, which corresponds to the radical of a nest algebra and describe it in a number of ways, generalizing known facts about nest algebras.
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套代数上的Jordan导子 总被引:10,自引:0,他引:10
本文主要研究套代数上的Jordan导子.证明了套代数上的任一Jordan导子都是内导子;作为应用最后讨论了套代数上的Jordan自同构. 相似文献
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Von Neumann代数中的套子代数 总被引:2,自引:1,他引:2
本文主要讨论因子Von Neumann代数中套子代数上的线性满等距和自伴导子.证明了因子Von Neumann代数中套子代数上的每个线性满等距是同构乘酉算子或者是反同构乘酉算子;给出了其上自伴导子是内导子的条件并得到有限因子 Von Neumann代数中套子代数上的每个自伴导子都是内导子. 相似文献
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P. A. Fillmore W. E. Longstaff G. W. MacDonald H. Radjavi Y. Zhong 《Linear algebra and its applications》2002,350(1-3):185-197
If
are maximal nests on a finite-dimensional Hilbert space H, the dimension of the intersection of the corresponding nest algebras is at least dim H. On the other hand, there are three maximal nests whose nest algebras intersect in the scalar operators. The dimension of the intersection of two nest algebras (corresponding to maximal nests) can be of any integer value from n to n(n+1)/2, where n=dim H. For any two maximal nests
there exists a basis {f1,f2,…,fn} of H and a permutation π such that
and
where Mi= span{f1,f2,…,fi} and Ni= span{fπ(1),fπ(2),…,fπ(i)}. The intersection of the corresponding nest algebras has minimum dimension, namely dim H, precisely when π(j)=n−j+1,1jn. Those algebras which are upper-triangular matrix incidence algebras, relative to some basis, can be characterised as intersections of certain nest algebras. 相似文献
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In this paper,linear maps preserving Lie products at zero points on nest algebras are studied.It is proved that every linear map preserving Lie products at zero points on any finite nest algebra is a Lie homomorphism.As an application,the form of a linear bijection preserving Lie products at zero points between two finite nest algebras is obtained. 相似文献
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本文给出套代数上保零积或者保多项式零化线性映射的刻画,从而得到其上自同构的一些新特征和原子套代数上保零积可加映射的完全分类. 相似文献
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Alan L. T. Paterson Roger R. Smith 《Transactions of the American Mathematical Society》1997,349(5):1919-1943
We investigate the cohomology of non-self-adjoint algebras using virtual diagonals and their higher-dimensional generalizations. We show that infinite dimensional nest algebras always have non-zero second cohomology by showing that they cannot possess 2-virtual diagonals. In the case of the upper triangular atomic nest algebra we exhibit concrete modules for non-vanishing cohomology.
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本文证明了:Banach空间上完全分配格代数间的导子都是自动连续的;进而证明了套代数的可加导子是内的,套代数间的代数同构是自动连续的、空间的 相似文献