[Merged by Bors] - feat(analysis/normed_space/basic): the left-regular representation is an isometry for (even non-unital) C⋆-algebras #16964
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Co-authored-by: Anatole Dedecker <anatolededecker@gmail.com>
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The import `analysis/normed_space/operator_norm` was added to this file by @j-loreaux in #16964, but nowadays `operator_norm` is quite a heavy import (it contains everything on the strong topologies, etc), whereas I hope that `normed_space/star/basic` can become a fairly lightweight one (because it is imported by `is_R_or_C` which is imported everywhere). I propose to split out the material from #16964.
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This is a key tool to show that the multiplier algebra is a C⋆-algebra.
densely_normed_fieldin terms of the supremum #16963Note: the
nnnormversions are provided for convenience of rewriting, whereas I did not provide thenormversion because they can be accessed via theisometrylemma, for example:(add_monoid_hom_class.isometry_iff_norm _).1 (mul_isometry 𝕜 E) a