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Similarity preserving linear maps on \({\mathscr {J}}\)-subspace lattice algebras

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Abstract

We describe the structure of similarity preserving linear maps of reflexive algebras with \({\mathscr {J}}\)-subspace lattices. This result can apply to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.

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Acknowledgements

The authors would like to thank the referee for a very thorough reading of the paper and many helpful comments. The research was supported by the National Natural Science Foundation of China (Grant No. 11571247).

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Authors and Affiliations

  1. Department of Mathematics, Soochow University, Suzhou, 215006, China

    Zijie Qin & Fangyan Lu

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  1. Zijie Qin
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  2. Fangyan Lu
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Correspondence to Fangyan Lu.

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Communicated by Gelu Popescu.

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Qin, Z., Lu, F. Similarity preserving linear maps on \({\mathscr {J}}\)-subspace lattice algebras. Banach J. Math. Anal. 14, 856–870 (2020). https://doi.org/10.1007/s43037-019-00042-0

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  • DOI: https://doi.org/10.1007/s43037-019-00042-0

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