2-Local isometries between Banach algebras of continuous functions with involution
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We give a description of 2-local real isometries between \(C(X,\tau )\) and \(C(Y,\eta )\) where X and Y are compact Hausdorff spaces, X is also first countable and \(\tau \) and \(\eta \) are topological involutions on X and Y, respectively. In particular, we show that every 2-local real isometry T from \(C(X,\tau )\) to \( C(Y,\eta )\) is a surjective real linear isometry whenever X is also separable.
KeywordsBanach algebra 2-Local real isometry Real linear isometry Topological involution
Mathematics Subject Classification47B38 46J10
The authors would like to thank the referee for his/her valuable comments and suggestions.
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