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On isometric stability of complemented subspaces of L p
Authors:Beata Randrianantoanina
Affiliation:(1) Department of Mathematics and Statistics, Miami University, 45056 Oxford, OH, USA
Abstract:We show that the Rudin-Plotkin isometry extension theorem inL pimplies that whenX andY are isometric subspaces ofL pandp is not an even integer, 1≤p<∞, thenX is complemented inL pif and only ifY is; moreover, the constants of complementation ofX andY are equal. We provide examples demonstrating that this fact fails whenp is an even integer larger than 2.
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