Operators preserving orthogonality are isometries
Alexander Koldobsky
Abstract
Let E be a real Banach space. For x,y ∈ E, we follow R.James in saying that x is orthogonal to y if \|x+αy\|≥ \|x\| for every α∈ R. We prove that every operator from E into itself preserving orthogonality is an isometry multiplied by a constant.
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