Commit 2022-10-24 21:05 b06d2285
View on Github →feat(analysis/normed_space/operator_norm): characterize the operator norm over a densely_normed_field
in terms of the supremum (#16963)
This provides a few results pertaining to the operator norm over a densely_normed_field
. In particular, if 0 ≤ r < ∥f∥
then there exists some x
with ∥x∥ ≤ 1
such that r < ∥f x∥
. Consequently, the operator norm is the supremum of the norm of the image of the unit ball under f
.