Displaying similar documents to “Absence of eigenvalues for integro-differential operators with periodic coefficients.”

Linear maps preserving the generalized spectrum.

Mostafa Mbekhta (2007)

Extracta Mathematicae

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Let H be an infinite-dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. For an operator T in B(H), let σ(T) denote the generalized spectrum of T. In this paper, we prove that if φ: B(H) → B(H) is a surjective linear map, then φ preserves the generalized spectrum (i.e. σ(φ(T)) = σ(T) for every T ∈ B(H)) if and only if there is A ∈ B(H) invertible such that either φ(T) = ATA for every T ∈ B(H), or φ(T) = ATA for every T ∈ B(H). Also,...