User:Lord Farin/Long-Term Projects/Conway Course

= Processing of 'A Course in Functional Analysis' =

$I.1.4$

Progress thus far
Celebration: Chapter $I$ covered! Lord_Farin 08:05, 16 January 2012 (EST)

Up to $II$ / p.26. Lord_Farin 04:00, 18 January 2012 (EST)

Up to $II.1.2$ / p.27. Lord_Farin 18:34, 23 January 2012 (EST)

Up to $II.2$ / p.31. Lord_Farin 08:55, 24 January 2012 (EST)

Up to $II.2.6$ / p.32. Lord_Farin 08:34, 27 January 2012 (EST)

Up to $II.2.7$ / p.32. Lord_Farin 08:36, 28 January 2012 (EST)

Up to $II.2.11$ / p.33. Lord_Farin 11:26, 30 January 2012 (EST)

Up to $II.2.17$ / p.35. Lord_Farin 05:09, 31 January 2012 (EST)

Up to $II.3$ / p.36. Lord_Farin 10:54, 31 January 2012 (EST)

Up to $II.3.3$ / p.37. Lord_Farin 10:35, 1 February 2012 (EST)

Up to $II.3.5$ / p.38. Lord_Farin 18:12, 2 February 2012 (EST)

Up to $II.3 \text{ Exercises}$ / p.40. Lord_Farin 10:42, 3 February 2012 (EST)

Up to $II.4$ / p.41. Lord_Farin 15:39, 14 February 2012 (EST)

Up to $II.4.6$ / p.42. Lord_Farin 09:18, 24 February 2012 (EST)

Up to $II.5$ / p.46. Lord_Farin 17:59, 27 February 2012 (EST)

Up to $II.6$ / p.49. Lord_Farin 05:41, 28 February 2012 (EST)

Skipped thus far (that is, what needs to be done still)

 * $I.1.7: \ell^2(I)$ (cf. also Ex. I.1.2)
 * $I.1.10-13: $ Bergman Spaces $L^2_a(G)$
 * $I.5.6-11:$ Rigorous foundations of Fourier analysis and $L^2_\C[0,2\pi]$.
 * $II.1.5:$ Bounded functions induce bounded linear operators on $L^2(\mu)$.
 * $II.1.6:$ Integral operators with certain kernels are bounded linear operators.
 * Maybe some more of $II.1 \text{ Exercises}, II.2 \text{ Exercises}$.
 * $II.2.8,9:$ Examples which are useful but their basis hasn't been covered.
 * $II.2.10:$ Unilateral shift on $\ell^2(\N)$
 * $II.4.7-8$: Integral operators with certain kernels are compact operators
 * $II.6$: Sturm-Liouville theory

Other things

 * Many of the proofs are missing; I generally put them in Category:Lord_Farin's Stubs.
 * Many of the pages now under Category:Hilbert Spaces can be generalized to Banach spaces. When this is covered, the pages will be put in appropriate category Category:Banach Spaces. There may come categories like Category:Operators on Banach Spaces in the future. --Lord_Farin 08:36, 28 January 2012 (EST)
 * The above idea for categories has largely been implemented. --Lord_Farin 14:02, 31 January 2012 (EST)
 * Some ideas came to mind constituting Bounded Linear Operators Form Monoid. In fact, they form a ring, and this will eventually lead to Banach algebras.