Zulip Chat Archive
Stream: Is there code for X?
Topic: Applying continuous linear map
Patrick Massot (Mar 21 2022 at 21:19):
I can't find:
variables
(𝕜 : Type*) (E : Type*) (F : Type*) [normed_group E]
[normed_group F] [nondiscrete_normed_field 𝕜]
[normed_space 𝕜 E] [normed_space 𝕜 F]
def continuous_linear_map.uncurry_apply : (E →L[𝕜] F) × E → F :=
λ p, p.1 p.2
lemma continuous_linear_map.is_bounded_bilinear_uncurry_apply :
is_bounded_bilinear_map 𝕜 (continuous_linear_map.uncurry_apply 𝕜 E F) :=
{ add_left := λ x φ ψ, continuous_linear_map.add_apply _ _ _,
smul_left := λ s x φ, rfl,
add_right := λ φ x y, φ.map_add x y,
smul_right := λ s φ x, φ.map_smul s x,
bound := ⟨1, zero_lt_one, λ φ x, by simpa using φ.le_op_norm x⟩ }
Where is it hidden?
Patrick Massot (Mar 21 2022 at 21:19):
Note that I found docs#continuous_linear_map.apply, but I didn't know how to convert it to the above.
Heather Macbeth (Mar 21 2022 at 21:23):
I think this is docs#is_bounded_bilinear_map_apply, right?
Patrick Massot (Mar 21 2022 at 21:31):
Yes!
Patrick Massot (Mar 21 2022 at 21:31):
Thanks!
Last updated: Dec 20 2023 at 11:08 UTC