Timeline for What (classes of) Banach spaces are known to have Schauder basis?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jul 6, 2013 at 4:04 | vote | accept | Clark Chong | ||
| Jun 27, 2013 at 2:04 | answer | added | Bill Johnson | timeline score: 12 | |
| Jun 26, 2013 at 22:00 | comment | added | Yemon Choi | The same goes for @PeterMichor | |
| Jun 26, 2013 at 21:59 | comment | added | Yemon Choi | I think @BillJohnson could leave his comments as an answer, since they seem to satisfy the OP's needs. | |
| Jun 26, 2013 at 21:05 | comment | added | Peter Michor | Check: MR0610799 Singer, Ivan Bases in Banach spaces. II. Editura Academiei Republicii Socialiste România, Bucharest; Springer-Verlag, Berlin-New York, 1981. viii+880 pp. ISBN: 3-540-10394-5 (Reviewer: Y. Benyamini) 46B15 (46-02) PDF Clipboard Series Book. MR0298399 Reviewed Singer, Ivan Bases in Banach spaces. I. Die Grundlehren der mathematischen Wissenschaften, Band 154. Springer-Verlag, New York-Berlin, 1970. viii+668 pp. (Reviewer: R. C. James) | |
| Jun 26, 2013 at 18:35 | history | edited | Clark Chong | CC BY-SA 3.0 |
added 175 characters in body
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| Jun 26, 2013 at 15:55 | comment | added | Bill Johnson | In [JRZ] you will find some results on when the $\pi$ property implies the existence of a finite dimensional decomposition and some results on the existence of bases, such as a separable complemented subspace of an $L+p$ space must have a Schauder basis. | |
| Jun 26, 2013 at 3:19 | comment | added | Clark Chong | Thanks Bill for pointing me to the references! I will check them out! I have also found this article of you which explains the $\pi$ property: link.springer.com/article/10.1007/BF02771464 | |
| Jun 25, 2013 at 20:17 | comment | added | Bill Johnson | For a good expository article, read Casazza's contribution in the Handbook of the Geometry of Banach Spaces, vol. 1. | |
| Jun 25, 2013 at 20:15 | comment | added | Bill Johnson | Most of the classical separable Banach spaces are known to have a Schauder basis. The book of Albiac and Kalton is good place to start. Singer's two volumes on bases in Banach spaces probably more than you would ever want to know. | |
| Jun 25, 2013 at 20:12 | comment | added | Bill Johnson | The property you define is usually called the $\Pi$ property. | |
| Jun 25, 2013 at 20:08 | history | asked | Clark Chong | CC BY-SA 3.0 |