On linear operators that preserve BJ-orthogonality in 2-normed space

Mahdi Iranmanesh, Ali Ganjbakhsh Sanatee

Abstract


Let X be a real 2-Banach space. We follow Gunawan,
Mashadi, Gemawati, Nursupiamin and Siwaningrum in saying that x is
orthogonal to y if there exists a subspace V of X with codim(V ) = 1
such that ∥x+λy; z∥ ≥ ∥x; z∥ for every z ∈ V and λ ∈ R. In this paper
we prove that every linear self mapping  T: X → X which preserve
orthogonality is a 2-isometry multiplied by a constant.

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