ε-orthogonality preserving pairs of mappings on Hilbert C*-modules

Document Type : Research Paper

Authors

1 Department of Mathematic, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

Abstract

Let A be a standard C∗-algebra. In this paper, we will study the continuity of ε-orthogonality preserving mappings between Hilbert A-modules. Moreover, we will show that a local mapping between Hilbert A-modules is  A-linear. Furthermore, we will prove that for a pair of nonzero A-linear mappings T,S:E⟶F, between Hilbert  A-modules, satisfying  ε-orthogonality preserving property, there exists γ∈C,
‖⟨T(x),S(y)⟩−γ⟨x,y⟩‖≤ε‖T‖‖S‖‖x‖‖y‖,x,y∈E.
Our results generalize the known ones in the context of Hilbert spaces.

Keywords

References

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Journal of Algebra and Related Topics
Volume 10, Issue 2
December 2022
Pages 51-60

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