On geometric structure of generalized projections in C*-algebras
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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.
Keywordsgeneralized projections Banach manifold geodesics
MSC(2010)32M10 53C22 53C30 47C15
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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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