Linear maps preserving the index of operators - Ragoubi, S. (Methods of Functional Analysis and Topology, 2017)
Let H be an infinite-dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. In this paper, we prove that if a surjective linear map φ : B(H) B(H) preserves the index of operators, then φ preserves compact operators in both directions and the induced map φ : C( H) C(H), determined by φ(π(T)) = π( φ(T)) for all T B(H), is a continuous automorphism multiplied by an invertible element in C( H).