Additive maps preserving the reduced minimum modulus of Banach space operators
Abdellatif Bourhim
Abstract:Let B(X) be the algebra of all bounded linear operators on an infinite dimensional complex Banach space X. We prove that an additive surjective map ϕ on B(X) preserves the reduced minimum modulus if and only if either there are bijective isometries U : X → X and V : X → X both linear or both conjugate linear such that ϕ(T ) = U T V for all T ∈ B(X), or X is reflexive and there are bijective isometries U : X * → X and V : X → X * both linear or both conjugate linear such that ϕ(T ) = U T * V for all T ∈ B(X). A… Show more
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