Resumen de Mappings preserving approximate orthogonality in Hilbert C∗-modules

Mohammad Sal Moslehian, Ali Zamani

• We introduce a notion of approximate orthogonality preserving mappings between Hilbert C∗-modules. We define the concept of (δ,ε) -orthogonality preserving mapping and give some sufficient conditions for a linear mapping to be (δ,ε)-orthogonality preserving. In particular, if E is a full Hilbert A-module with K(H)⊆A⊆B(H) and T,S:E→E are two linear mappings satisfying |⟨Sx,Sy⟩|=∥S∥2|⟨x,y⟩| for all x,y∈E and ∥T−S∥≤θ∥S∥, then we show that T is a (δ,ε)-orthogonality preserving mapping. We also prove whenever K(H)⊆A⊆B(H) and T:E→F is a nonzero A-linear (δ,ε)-orthogonality preserving mapping between A-modules, then ∥∥⟨Tx,Ty⟩−∥T∥2⟨x,y⟩∥∥≤4(ε−δ)(1−δ)(1+ε)∥Tx∥∥Ty∥(x,y∈E).

  As a result, we present some characterizations of the orthogonality preserving mappings