Let \(X\) and \(Y\) be normed spaces . A \(T\) bounded operator between \(X\) and \(Y\) is called linear isometry if
\[ \lVert Tx\rVert_Y=\lVert x\rVert_X \]for every \(x\in X\).
Remarks
- An isometry preserves length.
Let \(X\) and \(Y\) be normed spaces . A \(T\) bounded operator between \(X\) and \(Y\) is called linear isometry if
\[ \lVert Tx\rVert_Y=\lVert x\rVert_X \]for every \(x\in X\).