Commit Graph
100 Commits
Author SHA1 Message Date
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
Bokuan Li d4578960f3 Adjustments added to LCH spaces.
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2026-06-29 12:28:30 -04:00
Bokuan Li 17154547df More minor adjustments.
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2026-06-28 23:11:52 -04:00
Bokuan Li 35be74f8af Refined the approximation argument.
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2026-06-28 23:07:23 -04:00
Bokuan Li a7904bd32c More typo fix.
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2026-06-28 22:48:14 -04:00
Bokuan Li 06d3f994f6 Style adjustments in gluing lemma.
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2026-06-28 21:45:48 -04:00
Bokuan Li c484cd172b Typo fix.
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2026-06-28 21:33:06 -04:00
Bokuan Li 5abdf6ab3d Fixed wrong reference.
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2026-06-28 21:30:09 -04:00
Bokuan Li 8f06eca274 One more remark.
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2026-06-28 20:48:46 -04:00
Bokuan Li 145f3193be Minor sharpening of statements.
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2026-06-28 20:22:35 -04:00
Bokuan Li 2423cff867 Minor adjustment.
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2026-06-28 20:11:36 -04:00
Bokuan Li 3d1e095e82 Fixed typos in the gluing lemma.
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2026-06-28 20:10:25 -04:00
Bokuan Li 4226adf856 Added first darft of gluing lemma for measurable functions. 2026-06-28 19:50:05 -04:00
Bokuan Li 3a4f4b46e8 Added the theory of admissible approximant functions. 2026-06-28 19:29:22 -04:00
Bokuan Li 121033cfb6 Fixed label typo. 2026-06-28 14:35:23 -04:00
Bokuan Li 1d740724b4 Strengthened the simple function approximations. 2026-06-28 14:33:32 -04:00
Bokuan Li 4acc8fdf31 Un-retracted some things. 2026-06-28 12:05:22 -04:00
Bokuan Li bbff684bd1 Polish correction. 2026-06-28 12:04:51 -04:00
Bokuan Li 55bd2e4859 Fixed typo.
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2026-06-27 22:41:48 -04:00
Bokuan Li d8f56ef537 RETRACTION: SEPARABILITY REQUIRED TO DEFINE CONVERGENCE IN MEASURE 2026-06-27 22:38:39 -04:00
Bokuan Li ce52ac4b63 Edited the open preimage functions. 2026-06-27 22:35:32 -04:00
Bokuan Li 4616ac2861 First draft for open preimage functions. 2026-06-27 22:06:50 -04:00
Bokuan Li 80f79fb30d Added preimage functions. 2026-06-27 18:41:06 -04:00
Bokuan Li 48a0e63f61 Added elementary facts about localisable measure spaces. 2026-06-27 17:11:57 -04:00
Bokuan Li 3d9c47bda1 Minor housekeeping. 2026-06-27 14:12:40 -04:00
Bokuan Li 968fbe6eba Added the support function.
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2026-06-27 13:17:45 -04:00
Bokuan Li eed3a342e4 Typo fixes.
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2026-06-26 12:59:13 -04:00
Bokuan Li 369a1e72db Adjustment in Fenchl-Moreau. 2026-06-26 12:57:30 -04:00
Bokuan Li 03e7899904 Added the Mackey-Arens theorem (for real).
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2026-06-26 00:45:59 -04:00
Bokuan Li fbdf280f11 Fixed gap in maximum modulus strip. 2026-06-26 00:44:31 -04:00
Bokuan Li 91752ee561 Added compact definition.
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2026-06-26 00:17:28 -04:00
Bokuan Li 9c08e0a525 Added the Mackey-Arens theorem. 2026-06-26 00:16:36 -04:00
Bokuan Li 061a4f3034 More prose corrections.
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2026-06-25 19:22:37 -04:00
Bokuan Li 98f96b2af1 Performed more housekeeping for the Legendre transform.
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2026-06-25 19:16:16 -04:00
Bokuan Li 4b404d40a6 Updated the A-A theorem to include convergence on a dense subset.
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2026-06-25 13:58:38 -04:00
Bokuan Li b7f93c1110 Updated the legendre corollary.
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2026-06-25 13:32:44 -04:00
Bokuan Li 2c4a8c9d22 Typo fixes for the separable dual lemma.
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2026-06-25 13:17:05 -04:00
Bokuan Li 83072f4ba4 Adjusted the Legendre sectoin.
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2026-06-25 13:03:51 -04:00
Bokuan Li c19aaf7fe3 Fixed infinity problem. 2026-06-25 12:23:40 -04:00
Bokuan Li d857ff2bb7 Adjusted Fenchel's inequality. 2026-06-25 12:04:16 -04:00
Bokuan Li a1abb656f9 Updated convex characterisation. 2026-06-25 11:44:47 -04:00
Bokuan Li bc44e55e1d Renamed section. 2026-06-25 11:44:36 -04:00
Bokuan Li 7777095461 Added citations for elements taken from Cohn's Measure Theory.
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2026-06-24 23:28:30 -04:00
Bokuan Li 373bc8a223 Adjusted wording in Fenchel-Moreau.
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2026-06-24 23:21:52 -04:00
Bokuan Li e50cc6fb46 Updated gitignore. 2026-06-24 23:14:50 -04:00
Bokuan Li 460c84a483 Fixed up notation mistake.
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2026-06-24 22:36:08 -04:00
Bokuan Li 177ed32433 More typo fixes.
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2026-06-24 22:09:17 -04:00