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. ∥∥⟨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. 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. 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.

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