Abstract
Let \({\mathcal {B}}_{Id}({\mathcal {H}})\) be the set of all idempotents on a Hilbert space \({\mathcal {H}}.\) We give characterizations of the star partial order on \({\mathcal {B}}_{Id}({\mathcal {H}})\) with respect to a particular space decomposition, which is related to Halmos’ two projections theory. Using this, we investigate the lattice properties of \({\mathcal {B}}_{Id}({\mathcal {H}})\) endowed with the star partial order.
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22 June 2020
The original article has been corrected.
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Acknowledgements
The authors would like to express their heart-felt thanks to the anonymous referees for some valuable comments. The first named author was supported by NSF of China (No. 11601339). The second named author was supported by NSF of China (11671242, 11571211) and Fundamental Research Funds for the Central Universities (GK201801011).
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Communicated by Dragana Cvetkovic Ilic.
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Xu, XM., Li, Y. Star partial order on \({\mathcal {B}}_{Id}({\mathcal {H}})\). Ann. Funct. Anal. 11, 1093–1107 (2020). https://doi.org/10.1007/s43034-020-00073-x
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DOI: https://doi.org/10.1007/s43034-020-00073-x