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• 926305e65c Fixed typo. main Bokuan Li 2026-08-29 15:43:23 -04:00
• fab7bb7af4 Fixed citation entry for a stackexchange post. Bokuan Li 2026-08-28 15:06:30 -04:00
• f165b4fd2d Added citation for the type 1 proof. Bokuan Li 2026-08-27 20:30:50 -04:00
• f340ab9a29 Second draft of B(H). Bokuan Li 2026-08-27 18:20:28 -04:00
• dc9c66fe22 First draft of B(H). Bokuan Li 2026-08-27 17:36:32 -04:00
• 51d4752f4a Final review pass. Bokuan Li 2026-08-26 20:44:58 -04:00
• 67ccd97ac5 Another revision. Bokuan Li 2026-08-26 19:55:34 -04:00
• 4d7291bc9e Typo fixes in the type decomposition section. Bokuan Li 2026-08-26 19:32:11 -04:00
• fbf94061cb Typo fixes in projection section. Bokuan Li 2026-08-26 19:26:51 -04:00
• 1490514227 First draft of type decomposition. Bokuan Li 2026-08-26 19:25:58 -04:00
• 8f0998d52f Added projections. Bokuan Li 2026-08-24 17:41:04 -04:00
• fa4c1db319 Fixed a typo. Bokuan Li 2026-08-21 18:54:21 -04:00
• 881f4a4746 Editing. Bokuan Li 2026-08-20 16:25:48 -04:00
• b3d3620ec9 Added representation of commutative von Neumann algebras. Bokuan Li 2026-08-20 15:08:07 -04:00
• f65e49fccf Added some linfty. Bokuan Li 2026-08-18 21:47:50 -04:00
• e1fd4219a5 Added some applications of the $L^\infty$ functional calculus. Bokuan Li 2026-08-18 14:28:00 -04:00
• 5503003c92 Updated the spectral theorem. Bokuan Li 2026-08-17 00:24:34 -04:00
• 6cf96d9803 Fixed up spectral. Bokuan Li 2026-08-16 17:34:03 -04:00
• 0aa8e956f5 Fixed up the L^\infty functional calculus section. Bokuan Li 2026-08-16 16:22:23 -04:00
• 1b8d380eeb First typo fix of spectral II. Bokuan Li 2026-08-16 16:18:08 -04:00
• fa66eb73c9 First draft of spectral theorem II. Bokuan Li 2026-08-16 16:11:38 -04:00
• a98ff324ac Added another draft of the Borel functional calculus. Bokuan Li 2026-08-15 16:10:55 -04:00
• 51a74243a0 Added the spectral integral isomorphism. Bokuan Li 2026-08-15 15:34:26 -04:00
• 0cecf7a27a Fixed small typos. Bokuan Li 2026-08-14 20:54:09 -04:00
• 9530f806b1 Fixed some typos. Bokuan Li 2026-08-14 20:42:33 -04:00
• 421233bf4d Added first draft of the Borel functional calculus. Bokuan Li 2026-08-14 20:28:23 -04:00
• b51f12a338 Added the extended inverse Gelfand transform. Bokuan Li 2026-08-14 20:10:47 -04:00
• f8b61cca1a Updated $L^p$ notations. Bokuan Li 2026-08-14 14:29:06 -04:00
• e2eeae3f36 Fixed a few typos. Bokuan Li 2026-08-13 19:26:36 -04:00
• 1c33dabcd8 Trying to push again? Bokuan Li 2026-08-13 14:57:14 -04:00
• 4fb16feb5a Added the Arens extension. Bokuan Li 2026-08-13 14:27:43 -04:00
• 22a8d18845 Added trolling. Bokuan Li 2026-08-12 22:40:04 -04:00
• 594d139e4c Slight adjustments. Bokuan Li 2026-08-11 18:30:55 -04:00
• 05bc2c6820 Changed label format. Bokuan Li 2026-08-11 18:20:09 -04:00
• 2177baf09d Added the Kaplansky Density Theorem. Bokuan Li 2026-08-11 16:18:48 -04:00
• 7e78ce4ae1 Simplified the separable dual result. Bokuan Li 2026-08-11 13:50:38 -04:00
• 6a53d4d107 Added a continuity result in strong operator topology. Bokuan Li 2026-08-11 13:40:24 -04:00
• 5d8a956d0c Added the bicommutant theorem. Bokuan Li 2026-08-10 16:03:07 -04:00
• f327c5ab93 Fixed typo. Bokuan Li 2026-08-09 21:23:49 -04:00
• c02d873ddd Added bilinear forms. Bokuan Li 2026-08-09 21:18:50 -04:00
• 56d081628f Updated citation on the existence of projections. Bokuan Li 2026-08-09 16:08:57 -04:00
• 575cd66ad8 Added the existence of projections. Bokuan Li 2026-08-09 15:40:56 -04:00
• 1bc1b17fee Added elementary properties of adjoint maps. Bokuan Li 2026-08-08 19:39:18 -04:00
• ae2fc8147f Added basic topology facts about B(H). Bokuan Li 2026-08-08 16:01:28 -04:00
• 8a9ecc85f3 Added a bit of von Neumann. Bokuan Li 2026-08-08 15:49:56 -04:00
• 8efc71c1a1 Fixed some typos. Bokuan Li 2026-08-08 15:06:50 -04:00
• bc1aea01b3 Added quotients. Bokuan Li 2026-08-08 14:56:27 -04:00
• 83854cdc04 Added a section on non-unital C^*-algebras. Bokuan Li 2026-08-08 12:49:01 -04:00
• b75d97e94a Linked existence of the weak integral. Bokuan Li 2026-08-07 20:14:59 -04:00
• a57b88618f Added existence of the weak integral. Bokuan Li 2026-08-07 20:14:39 -04:00
• 39a16de049 I didn't have closed graph theorem? Bokuan Li 2026-08-07 19:31:19 -04:00
• 4d4789bd38 Random nonsense. Bokuan Li 2026-08-07 17:49:06 -04:00
• 8faaa8dab4 Added the injective tensor product. Bokuan Li 2026-08-07 15:50:54 -04:00
• 39086537c3 Fixed diagram. Bokuan Li 2026-08-06 16:20:33 -04:00
• 07bfef705e Added Banach-Mazur. Bokuan Li 2026-08-06 16:19:07 -04:00
• 3ba29569ef Added universality of the zero-dimensional spaces. Bokuan Li 2026-08-06 15:59:15 -04:00
• a493db41c9 Typo fix. Bokuan Li 2026-07-24 18:43:35 -04:00
• 22ce40afa2 Fixed minor typo. Bokuan Li 2026-07-21 20:56:11 -04:00
• 12bc7db736 Added Schauder bases. Bokuan Li 2026-07-20 23:47:02 -04:00
• 1ef1cde0b2 Added another corollary. Bokuan Li 2026-07-20 22:55:07 -04:00
• 6019461a9b Added corollaries. Bokuan Li 2026-07-20 22:40:36 -04:00
• 60f8fb94eb Added characterisation of the approximation property. Bokuan Li 2026-07-20 19:48:59 -04:00
• aa47453f25 Added Gantmacher's theorem. Bokuan Li 2026-07-20 17:00:46 -04:00
• 22f9bc219b Added tensor gymnastics. Bokuan Li 2026-07-20 12:58:27 -04:00
• 4b1a17c259 Added the c_0 sequence space and its duality result. Bokuan Li 2026-07-20 12:57:20 -04:00
• 25d3f4e8d2 Added Goldstine's Theorem. Bokuan Li 2026-07-17 18:49:11 -04:00
• 843631b024 Added the compact null sequence lemma. Bokuan Li 2026-07-17 14:29:04 -04:00
• fe557de4a6 Various additions. Bokuan Li 2026-07-16 13:49:27 -04:00
• 42eeae1679 Every product of nuclear spaces is nuclear. Bokuan Li 2026-07-15 17:16:40 -04:00
• 1038594584 Sums of nuclear spaces are nuclear. Bokuan Li 2026-07-15 17:03:51 -04:00
• db79f11991 Quotients of nuclear spaces are nuclear. Bokuan Li 2026-07-15 16:28:53 -04:00
• 11c969be61 Subspaces of nuclear spaces are nuclear. Bokuan Li 2026-07-15 15:14:02 -04:00
• d967ed933e Updated nuclear spaces. Bokuan Li 2026-07-14 20:48:33 -04:00
• f80c788ca2 Added nuclear spaces. Bokuan Li 2026-07-14 20:31:59 -04:00
• 6b640447fb Added the polar decomposition. Bokuan Li 2026-07-14 16:20:16 -04:00
• d1ddf9f64b Added nuclear operators. 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