Let \(T\colon X\to Y\) be a bounded operator . The operator norm of \(T\) is defined by \(\lVert T\rVert=\sup_{\lVert x\rVert=1} \lVert Tx\rVert\).
Remarks
- The operator norm is indeed a norm .
Let \(T\colon X\to Y\) be a bounded operator . The operator norm of \(T\) is defined by \(\lVert T\rVert=\sup_{\lVert x\rVert=1} \lVert Tx\rVert\).