Abstract
Let P, Q be two orthogonal projections and J be a symmetry such that \(JP=QJ\). Based on the block operator technique and Halmos’ CS decomposition, we devote to characterizing the pseudo-regularity of \({\mathcal {R}}(P)\) and \({\mathcal {R}}(Q)\). It is given the J-projection onto a regular complement of \({\mathcal {R}}(P)^{\circ }\) in \({\mathcal {R}}(P)\) (resp. \({\mathcal {R}}(Q)^{\circ }\) in \({\mathcal {R}}(Q)\)). Furthermore, the sets of J-normal projections onto \({\mathcal {R}}(P)\) and \({\mathcal {R}}(Q)\) are obtained.
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Acknowledgements
We are grateful to the referees for a careful reading of the paper and valuable suggestions. This work was completed with the supports of the NNSFs of China (Grant Nos. 11761052, 11862019), NSF of Inner Mongolia (Grant No. 2020ZD01), the Key Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application (Inner Mongolia Normal University), Ministry of Education (Grant No. 2023KFZD01) and Inner Mongolia Autonomous Region University Innovation Team Development Plan (Grant No. NMGIRT2317).
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Communicated by Dragana Cvetkovic Ilic.
This work was completed with the support of the NNSFs of China (Grant Nos. 11761052, 11862019), NSF of Inner Mongolia (Grant No. 2020ZD01), the Key Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application (Inner Mongolia Normal University), Ministry of Education) (Grant No. 2023KFZD01).
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Zhang, L., Hai, G. The pseudo-regularity of the range of orthogonal projections in Krein spaces. Ann. Funct. Anal. 15, 6 (2024). https://doi.org/10.1007/s43034-023-00307-8
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DOI: https://doi.org/10.1007/s43034-023-00307-8