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Metamath Proof Explorer
Description: A Hermitian operator is a Hilbert space operator (mapping).
(Contributed by NM, 19-Mar-2006) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Assertion |
hmopf |
⊢ ( 𝑇 ∈ HrmOp → 𝑇 : ℋ ⟶ ℋ ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
elhmop |
⊢ ( 𝑇 ∈ HrmOp ↔ ( 𝑇 : ℋ ⟶ ℋ ∧ ∀ 𝑥 ∈ ℋ ∀ 𝑦 ∈ ℋ ( 𝑥 ·ih ( 𝑇 ‘ 𝑦 ) ) = ( ( 𝑇 ‘ 𝑥 ) ·ih 𝑦 ) ) ) |
| 2 |
1
|
simplbi |
⊢ ( 𝑇 ∈ HrmOp → 𝑇 : ℋ ⟶ ℋ ) |