diff --git a/Nevanlinna/tensor.lean b/Nevanlinna/tensor.lean index e69de29..f805778 100644 --- a/Nevanlinna/tensor.lean +++ b/Nevanlinna/tensor.lean @@ -0,0 +1,47 @@ +import Mathlib.Analysis.InnerProductSpace.PiL2 + + +open RCLike Real Filter +open Topology ComplexConjugate +open LinearMap (BilinForm) +open TensorProduct +open InnerProductSpace +open Inner + + +example + {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E] + {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℝ F] + : 1 = 0 := by + + let e : E →ₗ[ℝ] E →ₗ[ℝ] ℝ := innerₗ E + let f : F →ₗ[ℝ] F →ₗ[ℝ] ℝ := innerₗ F + let e₂ := TensorProduct.map₂ e f + let l := TensorProduct.lid ℝ ℝ + + have : ∀ e1 e2 : E, ∀ f1 f2 : F, e₂ (e1 ⊗ f1) (e2 ⊗ f2) = + + let X : InnerProductSpace.Core ℝ (E ⊗[ℝ] F) := { + inner := by + intro a b + exact TensorProduct.lid ℝ ℝ ((TensorProduct.map₂ (innerₗ E) (innerₗ F)) a b) + conj_symm := by + simp + intro x y + + unfold innerₗ + + simp + sorry + nonneg_re := _ + definite := _ + add_left := _ + smul_left := _ + } + + let inner : E ⊗[𝕜] E → E ⊗[𝕜] E → 𝕜 := + --let x := TensorProduct.lift + --E.inner + --TensorProduct.map₂ + sorry + sorry \ No newline at end of file