Timeline for An amenable operator algebra has the total reduction property
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 13, 2021 at 16:25 | history | undeleted | Korn | ||
| Aug 13, 2021 at 16:25 | history | deleted | Korn | via Vote | |
| Aug 13, 2021 at 16:25 | history | undeleted | Korn | ||
| Aug 11, 2021 at 18:32 | history | deleted | Korn | via Vote | |
| Aug 10, 2021 at 16:56 | comment | added | Yemon Choi | Also, to elaborate on Taka's point that Prop 2.2 can be "proved directly": for most practical/intuitive purposes, the better definition of amenability for Banach algebras is in terms of the existence of bounded approximate diagonals. Once you have such gadgets, there is a simple way to use them to average projections to get projections which respect the algebra action, and hence get the (total) reduction property | |
| Aug 10, 2021 at 16:50 | comment | added | Yemon Choi | For the benefit of other readers: as Taka has pointed out, Theorem 2.1 characterizes the total reduction property in terms of the vanishing of certain degree-1 cohomology groups. The passage quoted above shows that amenability, as originally defined by Johnson, is equivalent to vanishing of an even larger class of degree-1 cohomology groups. | |
| Aug 10, 2021 at 2:07 | comment | added | Narutaka OZAWA | That's because the assumption of Theorem 2.1 is satisfied. (Also it's easy to show Proposition 2.2 directly.) | |
| Aug 9, 2021 at 22:50 | review | First posts | |||
| Aug 9, 2021 at 23:56 | |||||
| Aug 9, 2021 at 22:42 | history | asked | Korn | CC BY-SA 4.0 |