A note on Maps preserving the local spectral subspace ofskew-product of operators

Let B(H) be the algebra of all bounded linear operators on in nite-dimensional complexHilbert space H. For T ۲ B(H) and ۲ C, let HT (f g) denotes the local spectral subspaceof T associated with f g. We show that if an additive map φ : B(H) 􀀀! B(H) has a rangecontaining all operators of rank at most two and satis esHφ(T)φ(S) (f g) = HTS (f g)for all T; S ۲ B(H) and ۲ C, then there exist two unitary operators U and V in B(H)such that φ(T) = UTV for all T ۲ B(H). Also, we obtain some interesting results in thisdirection.

کلیدواژه ها:

Local spectrum ، Local spectral subspace ، Nonlinear preservers ، Rank-one oper-ators