On the Extension of Isometries between the Unit Spheres of a C∗-algebra and B(h)
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چکیده
Given two complex Hilbert spaces H and K, let S(B(H)) and S(B(K)) denote the unit spheres of the C∗-algebras B(H) and B(K) of all bounded linear operators on H and K, respectively. We prove that every surjective isometry f : S(B(K)) → S(B(H)) admits an extension to a surjective complex linear or conjugate linear isometry T : B(K) → B(H). This provides a positive answer to Tingley’s problem in the setting of B(H) spaces.
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تاریخ انتشار 2018