Abstract
Let H be a Hilbert space and A ⊆ B(H) a C*-subalgebra. This paper is devoted to studying the set GP of generalized projections in A from a differential geometric point of view, and mainly focuses on geodesic curves. We prove that the space GP is a C∞ Banach submanifold of A, and a homogeneous reductive space under the action of Banach Lie group U A of A. Moreover, we compute the geodesics of GP in a standard fashion, and prove that any generalized projection in a prescribed neighbourhood of p ∈ GP can be joined with p by a unique geodesic curve in GP.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 11371233). The authors thank the referees for their valuable comments and suggestions.
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Cui, M., Ji, G. On geometric structure of generalized projections in C*-algebras. Sci. China Math. 61, 1187–1200 (2018). https://doi.org/10.1007/s11425-017-9111-7
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DOI: https://doi.org/10.1007/s11425-017-9111-7