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Orthogonality and disjointness preserving linear maps between Fourier and FourierStieltjes algebras of locally compact groups

Anthony To-Ming Lau Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43653

Journal of Functional Analysis, 265, (4), 562-593, 2013.8
This paper is devoted to the study of orthogonality and disjointness preserving linear maps between Fourier and FourierStieltjes algebras of locally compact groups. We show that a linear bijection : A (G 1) A (G 2)(resp. : B (G 1) B (G 2)) between two Fourier algebras (resp. FourierStieltjes algebras) of locally compact groups will induce a topological group isomorphism between G 1 and G 2, provided that preserves both disjointness and some kind of orthogonality. This improves earlier results of JJ Font and MS Monfared, where amenability of the groups or continuity of the linear maps are assumed. We also study the structure of bounded and unbounded disjointness preserving linear functionals of Fourier algebras. In the development, general results about disjointness and orthogonality preserving linear maps between C-algebras, W-algebras and their preduals are obtained.
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@inproceedings{anthony2013orthogonality,
  title={Orthogonality and disjointness preserving linear maps between Fourier and FourierStieltjes algebras of locally compact groups},
  author={Anthony To-Ming Lau, and Ngai-Ching Wong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020205600781285182},
  booktitle={Journal of Functional Analysis},
  volume={265},
  number={4},
  pages={562-593},
  year={2013},
}
Anthony To-Ming Lau, and Ngai-Ching Wong. Orthogonality and disjointness preserving linear maps between Fourier and FourierStieltjes algebras of locally compact groups. 2013. Vol. 265. In Journal of Functional Analysis. pp.562-593. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020205600781285182.
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