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Mirrors > Home > MPE Home > Th. List > df-nmhm | Structured version Visualization version Unicode version |
Description: Define a normed module homomorphism, also known as a bounded linear operator. This is a module homomorphism (a linear function) such that the operator norm is finite, or equivalently there is a constant such that... (Contributed by Mario Carneiro, 18-Oct-2015.) |
Ref | Expression |
---|---|
df-nmhm | NMHom NrmMod NrmMod LMHom NGHom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnmhm 22511 | . 2 NMHom | |
2 | vs | . . 3 | |
3 | vt | . . 3 | |
4 | cnlm 22385 | . . 3 NrmMod | |
5 | 2 | cv 1482 | . . . . 5 |
6 | 3 | cv 1482 | . . . . 5 |
7 | clmhm 19019 | . . . . 5 LMHom | |
8 | 5, 6, 7 | co 6650 | . . . 4 LMHom |
9 | cnghm 22510 | . . . . 5 NGHom | |
10 | 5, 6, 9 | co 6650 | . . . 4 NGHom |
11 | 8, 10 | cin 3573 | . . 3 LMHom NGHom |
12 | 2, 3, 4, 4, 11 | cmpt2 6652 | . 2 NrmMod NrmMod LMHom NGHom |
13 | 1, 12 | wceq 1483 | 1 NMHom NrmMod NrmMod LMHom NGHom |
Colors of variables: wff setvar class |
This definition is referenced by: reldmnmhm 22517 isnmhm 22550 |
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