Timeline for Real-world example of a Banach *-algebra with a nonzero *-radical
Current License: CC BY-SA 4.0
7 events
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| May 27, 2020 at 5:28 | comment | added | Cameron Zwarich | Hey Yemon! The Volterra algebra is actually a pretty great example. I'm surprised it's not in Palmer volume 2 along with the others. The disc algebra example is 9.7.25 in Palmer, but it has a faithful *-representation. I'm curious whether there's a infinite-dimensional non-commutative example that isn't somehow based on a finite-dimensional or commutative example. Maybe a semigroup algebra of some kind? | |
| May 26, 2020 at 23:29 | comment | added | Yemon Choi | In similar vein, I vaguely recall that the disc algebra with involution given by "take complex conjugates of all the Taylor coefficients" has bad properties as a star-algebra, this crops up somewhere in Palmer vol 2 but unfortunately I don't have a copy at hand | |
| May 26, 2020 at 23:26 | comment | added | Yemon Choi | Hi Cam, is the Volterra algebra with conjugation of functions as the star-operation good enough? :) | |
| May 26, 2020 at 17:05 | comment | added | Cameron Zwarich | I guess I'll take what I can get, with the bare minimum being "not specifically constructed for the purpose of providing an example", but it would be nice if there was some application. My best hope for a fully "natural" example is an algebra constructed from a group that only has a zero *-radical when the group has some approximation property. | |
| May 26, 2020 at 16:58 | comment | added | Robert Israel | How do you define "real-world"? | |
| May 26, 2020 at 16:50 | history | edited | Martin Sleziak |
added the (examples) tag
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| May 26, 2020 at 16:45 | history | asked | Cameron Zwarich | CC BY-SA 4.0 |