Commit Graph

65 Commits

Author SHA1 Message Date
Bokuan Li
0cecf7a27a Fixed small typos.
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2026-08-14 20:54:09 -04:00
Bokuan Li
9530f806b1 Fixed some typos.
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2026-08-14 20:42:33 -04:00
Bokuan Li
421233bf4d Added first draft of the Borel functional calculus.
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2026-08-14 20:28:23 -04:00
Bokuan Li
b51f12a338 Added the extended inverse Gelfand transform. 2026-08-14 20:10:47 -04:00
Bokuan Li
22a8d18845 Added trolling. 2026-08-12 22:40:04 -04:00
Bokuan Li
05bc2c6820 Changed label format. 2026-08-11 18:20:09 -04:00
Bokuan Li
2177baf09d Added the Kaplansky Density Theorem.
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2026-08-11 16:18:48 -04:00
Bokuan Li
6a53d4d107 Added a continuity result in strong operator topology. 2026-08-11 13:40:24 -04:00
Bokuan Li
5d8a956d0c Added the bicommutant theorem.
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2026-08-10 16:03:07 -04:00
Bokuan Li
56d081628f Updated citation on the existence of projections. 2026-08-09 16:08:57 -04:00
Bokuan Li
575cd66ad8 Added the existence of projections.
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2026-08-09 15:40:56 -04:00
Bokuan Li
1bc1b17fee Added elementary properties of adjoint maps.
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2026-08-08 19:39:18 -04:00
Bokuan Li
ae2fc8147f Added basic topology facts about B(H).
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2026-08-08 16:01:28 -04:00
Bokuan Li
8a9ecc85f3 Added a bit of von Neumann. 2026-08-08 15:49:56 -04:00
Bokuan Li
8efc71c1a1 Fixed some typos.
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2026-08-08 15:06:50 -04:00
Bokuan Li
bc1aea01b3 Added quotients. 2026-08-08 14:56:27 -04:00
Bokuan Li
83854cdc04 Added a section on non-unital C^*-algebras.
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2026-08-08 12:49:01 -04:00
Bokuan Li
a493db41c9 Typo fix.
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2026-07-24 18:43:35 -04:00
Bokuan Li
6b640447fb Added the polar decomposition. 2026-07-14 16:20:16 -04:00
Bokuan Li
84316a2059 Fiest draft of nuclear operators. 2026-07-13 15:26:05 -04:00
Bokuan Li
d0f646fbe1 Added GNS.
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2026-07-09 15:31:43 -04:00
Bokuan Li
013b095fa2 Added setup for GNS. 2026-07-09 12:36:43 -04:00
Bokuan Li
897edcf512 Added explicit descriptions of states in matrix algebras.
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2026-07-08 17:16:27 -04:00
Bokuan Li
709ce33a8d Minor cleanup.
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2026-07-08 15:16:14 -04:00
Bokuan Li
e5ef0d51df Added states.
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2026-07-08 15:02:23 -04:00
Bokuan Li
bf0107f15d Oopsies daisies.
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2026-07-07 20:50:19 -04:00
Bokuan Li
22ed76cb00 Word massaging.
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2026-07-07 17:40:49 -04:00
Bokuan Li
de9b6fb813 Added characterisation of positive linear functionals.
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2026-07-07 17:26:52 -04:00
Bokuan Li
f4e5004e8c Added remark. 2026-07-07 12:34:05 -04:00
Bokuan Li
f3c2c97f3b Added order decomposition for C*-algebras. 2026-07-07 12:33:11 -04:00
Bokuan Li
2ce66064fe Added continuity of homomorphisms.
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2026-07-07 12:09:59 -04:00
Bokuan Li
f613e65d10 Removed parts from Zhu citations. 2026-07-07 11:39:54 -04:00
Bokuan Li
86aba8ee4b Minor adjustments. 2026-07-06 12:36:34 -04:00
Bokuan Li
2cf172fa34 Fixed typo.
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2026-07-04 12:53:34 -04:00
Bokuan Li
9963459363 Finished lecture 11.
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2026-07-03 16:55:00 -04:00
Bokuan Li
26fdb527ce Added more facts about the positive square root.
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2026-07-03 16:20:41 -04:00
Bokuan Li
35e9550ff2 Added the continuous functional calculus. 2026-07-03 15:21:33 -04:00
Bokuan Li
683b822e7e Added Gelfand Naimark.
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2026-07-02 14:02:26 -04:00
Bokuan Li
60544ea6a0 Added some spectrum gruntwork. 2026-06-30 16:12:33 -04:00
Bokuan Li
99d772d1c8 Added the Riesz decomposition.
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2026-06-05 21:57:02 -04:00
Bokuan Li
09a94756ea Added basics of C*-algebras.
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2026-06-04 17:54:06 -04:00
Bokuan Li
2444406ec1 Added facts about C_0. 2026-06-04 16:31:26 -04:00
Bokuan Li
13a0e07b72 Fixed some numbering problems. 2026-06-04 13:41:05 -04:00
Bokuan Li
ebead6c022 Added the unitisation. 2026-06-04 13:39:55 -04:00
Bokuan Li
6441352421 Fixed wrong proof marker.
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2026-06-03 17:24:30 -04:00
Bokuan Li
677a396e24 Fixed missing citation.
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2026-06-03 17:13:07 -04:00
Bokuan Li
6c9c479198 Adjusted prose in example facts.
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2026-06-03 17:08:55 -04:00
Bokuan Li
668679063b Added some example facts. 2026-06-03 16:56:40 -04:00
Bokuan Li
f72f815c72 Added basic facts about the Gelfand transform. 2026-06-03 15:44:13 -04:00
Bokuan Li
56f3ae37f7 Slight adjustments in known results. 2026-06-03 14:37:13 -04:00