Commit Graph
100 Commits
Author SHA1 Message Date
Bokuan Li a98ff324ac Added another draft of the Borel functional calculus.
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2026-08-15 16:10:55 -04:00
Bokuan Li 51a74243a0 Added the spectral integral isomorphism. 2026-08-15 15:34:26 -04:00
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 f8b61cca1a Updated $L^p$ notations. 2026-08-14 14:29:06 -04:00
Bokuan Li e2eeae3f36 Fixed a few typos.
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2026-08-13 19:26:36 -04:00
Bokuan Li 1c33dabcd8 Trying to push again?
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2026-08-13 14:57:14 -04:00
Bokuan Li 4fb16feb5a Added the Arens extension.
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2026-08-13 14:27:43 -04:00
Bokuan Li 22a8d18845 Added trolling. 2026-08-12 22:40:04 -04:00
Bokuan Li 594d139e4c Slight adjustments.
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2026-08-11 18:30:55 -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 7e78ce4ae1 Simplified the separable dual result. 2026-08-11 13:50:38 -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 f327c5ab93 Fixed typo.
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2026-08-09 21:23:49 -04:00
Bokuan Li c02d873ddd Added bilinear forms.
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2026-08-09 21:18:50 -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 b75d97e94a Linked existence of the weak integral.
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2026-08-07 20:14:59 -04:00
Bokuan Li a57b88618f Added existence of the weak integral. 2026-08-07 20:14:39 -04:00
Bokuan Li 39a16de049 I didn't have closed graph theorem? 2026-08-07 19:31:19 -04:00
Bokuan Li 4d4789bd38 Random nonsense.
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2026-08-07 17:49:06 -04:00
Bokuan Li 8faaa8dab4 Added the injective tensor product.
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2026-08-07 15:50:54 -04:00
Bokuan Li 39086537c3 Fixed diagram.
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2026-08-06 16:20:33 -04:00
Bokuan Li 07bfef705e Added Banach-Mazur. 2026-08-06 16:19:07 -04:00
Bokuan Li 3ba29569ef Added universality of the zero-dimensional spaces. 2026-08-06 15:59:15 -04:00
Bokuan Li a493db41c9 Typo fix.
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2026-07-24 18:43:35 -04:00
Bokuan Li 22ce40afa2 Fixed minor typo.
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2026-07-21 20:56:11 -04:00
Bokuan Li 12bc7db736 Added Schauder bases.
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2026-07-20 23:47:02 -04:00
Bokuan Li 1ef1cde0b2 Added another corollary.
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2026-07-20 22:55:07 -04:00
Bokuan Li 6019461a9b Added corollaries.
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2026-07-20 22:40:36 -04:00
Bokuan Li 60f8fb94eb Added characterisation of the approximation property.
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2026-07-20 19:48:59 -04:00
Bokuan Li aa47453f25 Added Gantmacher's theorem.
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2026-07-20 17:00:46 -04:00
Bokuan Li 22f9bc219b Added tensor gymnastics. 2026-07-20 12:58:27 -04:00
Bokuan Li 4b1a17c259 Added the c_0 sequence space and its duality result. 2026-07-20 12:57:20 -04:00
Bokuan Li 25d3f4e8d2 Added Goldstine's Theorem.
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2026-07-17 18:49:11 -04:00
Bokuan Li 843631b024 Added the compact null sequence lemma. 2026-07-17 14:29:04 -04:00
Bokuan Li fe557de4a6 Various additions. 2026-07-16 13:49:27 -04:00
Bokuan Li 42eeae1679 Every product of nuclear spaces is nuclear.
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2026-07-15 17:16:40 -04:00
Bokuan Li 1038594584 Sums of nuclear spaces are nuclear. 2026-07-15 17:03:51 -04:00
Bokuan Li db79f11991 Quotients of nuclear spaces are nuclear. 2026-07-15 16:28:53 -04:00
Bokuan Li 11c969be61 Subspaces of nuclear spaces are nuclear. 2026-07-15 15:14:02 -04:00
Bokuan Li d967ed933e Updated nuclear spaces.
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2026-07-14 20:48:33 -04:00
Bokuan Li f80c788ca2 Added nuclear spaces.
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2026-07-14 20:31:59 -04:00
Bokuan Li 6b640447fb Added the polar decomposition. 2026-07-14 16:20:16 -04:00
Bokuan Li d1ddf9f64b Added nuclear operators.
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2026-07-13 15:36:06 -04:00
Bokuan Li 84316a2059 Fiest draft of nuclear operators. 2026-07-13 15:26:05 -04:00
Bokuan Li 3113e1da04 Fixed typo.
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2026-07-10 18:38:50 -04:00
Bokuan Li 97150879d7 Oopsies daisies.
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2026-07-10 13:19:12 -04:00
Bokuan Li d0f646fbe1 Added GNS.
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2026-07-09 15:31:43 -04:00
Bokuan Li 965a89d63a Fix typo in hahn-banach.
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2026-07-09 13:47:24 -04:00
Bokuan Li 67b00db276 Fix typo.
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2026-07-09 12:47:54 -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 0a288cda5d Updated main page.
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2026-07-07 22:08:29 -04:00
Bokuan Li bf0107f15d Oopsies daisies.
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2026-07-07 20:50:19 -04:00
Bokuan Li c7cca8820c Added Krein-Milman for measures. 2026-07-07 20:49:57 -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 f5ebcd7979 Reworked the order chapter. 2026-07-07 14:40:27 -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 dd62fbc0f4 Label typo? 2026-07-02 13:12:05 -04:00
Bokuan Li 1caa2785ef Small adjustments.
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2026-07-01 00:04:11 -04:00
Bokuan Li 89ec2234be Fixed typo.
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2026-06-30 19:34:11 -04:00
Bokuan Li 1f9e0bea78 Added extremely disconnected spaces.
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2026-06-30 19:32:42 -04:00
Bokuan Li 36f5b22042 Added localisable order completeness.
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2026-06-30 16:47:50 -04:00
Bokuan Li 60544ea6a0 Added some spectrum gruntwork. 2026-06-30 16:12:33 -04:00
Bokuan Li e19a5e3ad0 Swapped in vocabulary.
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2026-06-30 14:14:44 -04:00
Bokuan Li 8090f060d3 Added local L^p spaces. 2026-06-30 14:13:58 -04:00
Bokuan Li 98127388ec Retracted localisable version of Radon-Nikodym. 2026-06-30 13:42:43 -04:00
Bokuan Li baa048507b Added the localisable version of the radon-nikodym theorem.
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2026-06-29 21:29:57 -04:00
Bokuan Li 1ab81b49bc RETRACTION ON LCH EMBARRASSING TYPO
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2026-06-29 21:07:59 -04:00
Bokuan Li 38099f1b19 Added elements of localisable measures. 2026-06-29 20:55:01 -04:00
Bokuan Li 831acc66cc Added gluing for measures in terms of scaffoldings. 2026-06-29 19:29:18 -04:00
Bokuan Li 26c4bbbb51 LCH typo fix? 2026-06-29 19:09:55 -04:00
Bokuan Li ff22fad2f8 Updated the existing system to accomodate scaffolds.
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2026-06-29 17:43:02 -04:00
Bokuan Li 3ba0eee08d Introduced scaffold to localisable measure spaces. 2026-06-29 16:57:59 -04:00
Bokuan Li 671e8984c7 Added the scaffold. 2026-06-29 16:49:35 -04:00
Bokuan Li a11cfe4e04 Book keeping. 2026-06-29 16:34:06 -04:00
Bokuan Li 65a2b4cef4 FIxed up lattices.
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2026-06-29 12:37:13 -04:00