[Merged by Bors] - feat(algebra/star/unitary): (re)define unitary elements of a star monoid #11457
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I went ahead and pushed my golfing suggestions, since it was easier than adding github comments - hope that's ok! |
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(@eric-wieser it seems your golfs broke the build) |
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Thanks -- the changes look good! |
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Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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✌️ dupuisf can now approve this pull request. To approve and merge a pull request, simply reply with |
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Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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…oid (#11457) This PR defines `unitary R` for a star monoid `R` as the submonoid containing the elements that satisfy both `star U * U = 1` and `U * star U = 1`. We show basic properties (i.e. that this forms a group) and show that they preserve the norm when `R` is a C* ring. Note that this replaces `unitary_submonoid`, which only included the condition `star U * U = 1` -- see [the discussion](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/unitary.20submonoid) on Zulip. Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Frédéric Dupuis <31101893+dupuisf@users.noreply.github.com>
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This PR defines
unitary Rfor a star monoidRas the submonoid containing the elements that satisfy bothstar U * U = 1andU * star U = 1. We show basic properties (i.e. that this forms a group) and show that theypreserve the norm when
Ris a C* ring.Note that this replaces
unitary_submonoid, which only included the conditionstar U * U = 1-- see the discussion on Zulip.