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• d1ddf9f64b Added nuclear operators. main Bokuan Li 2026-07-13 15:36:06 -04:00
• 84316a2059 Fiest draft of nuclear operators. Bokuan Li 2026-07-13 15:26:05 -04:00
• 3113e1da04 Fixed typo. Bokuan Li 2026-07-10 18:38:50 -04:00
• 97150879d7 Oopsies daisies. Bokuan Li 2026-07-10 13:19:12 -04:00
• d0f646fbe1 Added GNS. Bokuan Li 2026-07-09 15:31:43 -04:00
• 965a89d63a Fix typo in hahn-banach. Bokuan Li 2026-07-09 13:47:24 -04:00
• 67b00db276 Fix typo. Bokuan Li 2026-07-09 12:47:54 -04:00
• 013b095fa2 Added setup for GNS. Bokuan Li 2026-07-09 12:36:43 -04:00
• 897edcf512 Added explicit descriptions of states in matrix algebras. Bokuan Li 2026-07-08 17:16:27 -04:00
• 709ce33a8d Minor cleanup. Bokuan Li 2026-07-08 15:16:14 -04:00
• e5ef0d51df Added states. Bokuan Li 2026-07-08 15:02:23 -04:00
• 0a288cda5d Updated main page. Bokuan Li 2026-07-07 22:08:29 -04:00
• bf0107f15d Oopsies daisies. Bokuan Li 2026-07-07 20:50:19 -04:00
• c7cca8820c Added Krein-Milman for measures. Bokuan Li 2026-07-07 20:49:57 -04:00
• 22ed76cb00 Word massaging. Bokuan Li 2026-07-07 17:40:49 -04:00
• de9b6fb813 Added characterisation of positive linear functionals. Bokuan Li 2026-07-07 17:26:52 -04:00
• f5ebcd7979 Reworked the order chapter. Bokuan Li 2026-07-07 14:40:27 -04:00
• f4e5004e8c Added remark. Bokuan Li 2026-07-07 12:34:05 -04:00
• f3c2c97f3b Added order decomposition for C*-algebras. Bokuan Li 2026-07-07 12:33:11 -04:00
• 2ce66064fe Added continuity of homomorphisms. Bokuan Li 2026-07-07 12:09:59 -04:00
• f613e65d10 Removed parts from Zhu citations. Bokuan Li 2026-07-07 11:39:54 -04:00
• 86aba8ee4b Minor adjustments. Bokuan Li 2026-07-06 12:36:34 -04:00
• 2cf172fa34 Fixed typo. Bokuan Li 2026-07-04 12:53:34 -04:00
• 9963459363 Finished lecture 11. Bokuan Li 2026-07-03 16:55:00 -04:00
• 26fdb527ce Added more facts about the positive square root. Bokuan Li 2026-07-03 16:20:41 -04:00
• 35e9550ff2 Added the continuous functional calculus. Bokuan Li 2026-07-03 15:21:33 -04:00
• 683b822e7e Added Gelfand Naimark. Bokuan Li 2026-07-02 14:02:26 -04:00
• dd62fbc0f4 Label typo? Bokuan Li 2026-07-02 13:12:05 -04:00
• 1caa2785ef Small adjustments. Bokuan Li 2026-07-01 00:04:11 -04:00
• 89ec2234be Fixed typo. Bokuan Li 2026-06-30 19:34:11 -04:00
• 1f9e0bea78 Added extremely disconnected spaces. Bokuan Li 2026-06-30 19:32:42 -04:00
• 36f5b22042 Added localisable order completeness. Bokuan Li 2026-06-30 16:47:50 -04:00
• 60544ea6a0 Added some spectrum gruntwork. Bokuan Li 2026-06-30 16:12:33 -04:00
• e19a5e3ad0 Swapped in vocabulary. Bokuan Li 2026-06-30 14:14:44 -04:00
• 8090f060d3 Added local L^p spaces. Bokuan Li 2026-06-30 14:13:58 -04:00
• 98127388ec Retracted localisable version of Radon-Nikodym. Bokuan Li 2026-06-30 13:42:43 -04:00
• baa048507b Added the localisable version of the radon-nikodym theorem. Bokuan Li 2026-06-29 21:29:57 -04:00
• 1ab81b49bc RETRACTION ON LCH EMBARRASSING TYPO Bokuan Li 2026-06-29 21:07:59 -04:00
• 38099f1b19 Added elements of localisable measures. Bokuan Li 2026-06-29 20:55:01 -04:00
• 831acc66cc Added gluing for measures in terms of scaffoldings. Bokuan Li 2026-06-29 19:29:18 -04:00
• 26c4bbbb51 LCH typo fix? Bokuan Li 2026-06-29 19:09:55 -04:00
• ff22fad2f8 Updated the existing system to accomodate scaffolds. Bokuan Li 2026-06-29 17:43:02 -04:00
• 3ba0eee08d Introduced scaffold to localisable measure spaces. Bokuan Li 2026-06-29 16:57:59 -04:00
• 671e8984c7 Added the scaffold. Bokuan Li 2026-06-29 16:49:35 -04:00
• a11cfe4e04 Book keeping. Bokuan Li 2026-06-29 16:34:06 -04:00
• 65a2b4cef4 FIxed up lattices. Bokuan Li 2026-06-29 12:37:13 -04:00
• d4578960f3 Adjustments added to LCH spaces. Bokuan Li 2026-06-29 12:28:30 -04:00
• 17154547df More minor adjustments. Bokuan Li 2026-06-28 23:11:52 -04:00
• 35be74f8af Refined the approximation argument. Bokuan Li 2026-06-28 23:07:23 -04:00
• a7904bd32c More typo fix. Bokuan Li 2026-06-28 22:48:14 -04:00
• 06d3f994f6 Style adjustments in gluing lemma. Bokuan Li 2026-06-28 21:45:48 -04:00
• c484cd172b Typo fix. Bokuan Li 2026-06-28 21:33:06 -04:00
• 5abdf6ab3d Fixed wrong reference. Bokuan Li 2026-06-28 21:30:09 -04:00
• 8f06eca274 One more remark. Bokuan Li 2026-06-28 20:48:46 -04:00
• 145f3193be Minor sharpening of statements. Bokuan Li 2026-06-28 20:22:35 -04:00
• 2423cff867 Minor adjustment. Bokuan Li 2026-06-28 20:11:36 -04:00
• 3d1e095e82 Fixed typos in the gluing lemma. Bokuan Li 2026-06-28 20:10:25 -04:00
• 4226adf856 Added first darft of gluing lemma for measurable functions. Bokuan Li 2026-06-28 19:50:05 -04:00
• 3a4f4b46e8 Added the theory of admissible approximant functions. Bokuan Li 2026-06-28 19:29:22 -04:00
• 121033cfb6 Fixed label typo. Bokuan Li 2026-06-28 14:35:23 -04:00
• 1d740724b4 Strengthened the simple function approximations. Bokuan Li 2026-06-28 14:33:32 -04:00
• 4acc8fdf31 Un-retracted some things. Bokuan Li 2026-06-28 12:05:22 -04:00
• bbff684bd1 Polish correction. Bokuan Li 2026-06-28 12:04:51 -04:00
• 55bd2e4859 Fixed typo. Bokuan Li 2026-06-27 22:41:48 -04:00
• d8f56ef537 RETRACTION: SEPARABILITY REQUIRED TO DEFINE CONVERGENCE IN MEASURE Bokuan Li 2026-06-27 22:38:39 -04:00
• ce52ac4b63 Edited the open preimage functions. Bokuan Li 2026-06-27 22:35:32 -04:00
• 4616ac2861 First draft for open preimage functions. Bokuan Li 2026-06-27 22:06:50 -04:00
• 80f79fb30d Added preimage functions. Bokuan Li 2026-06-27 18:41:06 -04:00
• 48a0e63f61 Added elementary facts about localisable measure spaces. Bokuan Li 2026-06-27 17:11:57 -04:00
• 3d9c47bda1 Minor housekeeping. Bokuan Li 2026-06-27 14:12:40 -04:00
• 968fbe6eba Added the support function. Bokuan Li 2026-06-27 13:17:45 -04:00
• eed3a342e4 Typo fixes. Bokuan Li 2026-06-26 12:59:13 -04:00
• 369a1e72db Adjustment in Fenchl-Moreau. Bokuan Li 2026-06-26 12:57:30 -04:00
• 03e7899904 Added the Mackey-Arens theorem (for real). Bokuan Li 2026-06-26 00:45:59 -04:00
• fbdf280f11 Fixed gap in maximum modulus strip. Bokuan Li 2026-06-26 00:44:31 -04:00
• 91752ee561 Added compact definition. Bokuan Li 2026-06-26 00:17:28 -04:00
• 9c08e0a525 Added the Mackey-Arens theorem. Bokuan Li 2026-06-26 00:16:36 -04:00
• 061a4f3034 More prose corrections. Bokuan Li 2026-06-25 19:22:37 -04:00
• 98f96b2af1 Performed more housekeeping for the Legendre transform. Bokuan Li 2026-06-25 19:16:16 -04:00
• 4b404d40a6 Updated the A-A theorem to include convergence on a dense subset. Bokuan Li 2026-06-25 13:58:38 -04:00
• b7f93c1110 Updated the legendre corollary. Bokuan Li 2026-06-25 13:32:44 -04:00
• 2c4a8c9d22 Typo fixes for the separable dual lemma. Bokuan Li 2026-06-25 13:17:05 -04:00
• 83072f4ba4 Adjusted the Legendre sectoin. Bokuan Li 2026-06-25 13:03:51 -04:00
• c19aaf7fe3 Fixed infinity problem. Bokuan Li 2026-06-25 12:23:40 -04:00
• d857ff2bb7 Adjusted Fenchel's inequality. Bokuan Li 2026-06-25 12:04:16 -04:00
• a1abb656f9 Updated convex characterisation. Bokuan Li 2026-06-25 11:44:47 -04:00
• bc44e55e1d Renamed section. Bokuan Li 2026-06-25 11:44:36 -04:00
• 7777095461 Added citations for elements taken from Cohn's Measure Theory. Bokuan Li 2026-06-24 23:28:30 -04:00
• 373bc8a223 Adjusted wording in Fenchel-Moreau. Bokuan Li 2026-06-24 23:21:52 -04:00
• e50cc6fb46 Updated gitignore. Bokuan Li 2026-06-24 23:14:50 -04:00
• 460c84a483 Fixed up notation mistake. Bokuan Li 2026-06-24 22:36:08 -04:00
• 177ed32433 More typo fixes. Bokuan Li 2026-06-24 22:09:17 -04:00
• c81b77a721 Added the separable corollary to the Legendre transform. Bokuan Li 2026-06-24 22:06:22 -04:00
• c897b3022e Fixed sign typo in Fenchel-Moreau. Bokuan Li 2026-06-24 21:55:34 -04:00
• 81e4ef6ffe Updated notation and formulation in the Fenchel Moreau theorem. Bokuan Li 2026-06-24 21:44:58 -04:00
• 9b6385cc16 Fixed typo in Fenchel-Moreau. Bokuan Li 2026-06-24 19:48:55 -04:00
• 32ba2483ad Added the Legendre transform. Bokuan Li 2026-06-24 18:29:26 -04:00
• a9890cbcab Added the subdifferential. Bokuan Li 2026-06-24 14:18:59 -04:00
• b20ae09a0c Fixed up convention in convex functions. Bokuan Li 2026-06-24 14:18:45 -04:00
• cddd7a4d55 Cleaned up citation stlye changes. Bokuan Li 2026-06-24 14:18:27 -04:00