Description: The norm of an operator composed with its adjoint. Part of Theorem 3.11(vi) of Beran p. 106. (Contributed by NM, 10-Mar-2006) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | nmopcoadj.1 | |
|
Assertion | nmopcoadj2i | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nmopcoadj.1 | |
|
2 | adjbdln | |
|
3 | 1 2 | ax-mp | |
4 | 3 | nmopcoadji | |
5 | bdopadj | |
|
6 | 1 5 | ax-mp | |
7 | adjadj | |
|
8 | 6 7 | ax-mp | |
9 | 8 | coeq1i | |
10 | 9 | fveq2i | |
11 | 1 | nmopadji | |
12 | 11 | oveq1i | |
13 | 4 10 12 | 3eqtr3i | |