Single elements and module isomorphisms of some operator algebra modules
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- by Dong Zhe PDF
- Proc. Amer. Math. Soc. 135 (2007), 191-200 Request permission
Abstract:
In this paper, we first introduce the concept of single elements in a module. A systematic study of single elements in the $\mbox {Alg}\mathcal {L}$-module $\mathcal {U}$ is initiated, where $\mathcal {L}$ is a completely distributive subspace lattice on a Hilbert space ${\mathcal H}$. Furthermore, as an application of single elements, we study module isomorphisms between norm closed $\mbox {Alg}\mathcal {N}$-modules, where $\mathcal {N}$ is a nest, and obtain the following result: Suppose that $\mathcal {U}, \mathcal {V}$ are norm closed $\mbox {Alg}\mathcal {N}$-modules and that $\Phi : \mathcal {U}\rightarrow \mathcal {V}$ is a module isomorphism. Then $\mathcal {U}=\mathcal {V}$ and there exists a non-zero complex number $\lambda$ such that $\Phi (T)=\lambda T, \forall T\in \mathcal {U}$.References
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Additional Information
- Dong Zhe
- Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China
- Email: dongzhe@zju.edu.cn
- Received by editor(s): November 3, 2004
- Received by editor(s) in revised form: July 30, 2005
- Published electronically: June 22, 2006
- Additional Notes: This project was partially supported by the National Natural Science Foundation of China (No. 10401030), the Zhejiang Natural Science Foundation (No. M103044) and GFJG
- Communicated by: David R. Larson
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 191-200
- MSC (2000): Primary 47L75
- DOI: https://doi.org/10.1090/S0002-9939-06-08468-1
- MathSciNet review: 2280187