Timeline for Operator norm of shift operator for finite measure spaces
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 5, 2020 at 19:48 | comment | added | Nik Weaver | But it's easy enough to come up with an $h$ such that the norms tend to $1$ as $a \to 0$. | |
| Jun 5, 2020 at 19:48 | comment | added | Nik Weaver | No, not possible. Whatever $a$ is, you can find a positive measure ball which is small enough that it is disjoint from its translation by $a$. So if you translate it by $na$ for all $n \in \mathbb{Z}$ you get an infinite sequence of disjoint sets and finiteness of $\nu$ implies that they can't all have the same measure. | |
| Jun 5, 2020 at 17:04 | comment | added | ABIM | I've been thinking about it but is even possible to have a probability measure $\nu$ and some $a \in \mathbb{R}^n-\{0\}$ for which $\sqrt{\frac{\|h_a\|}{\|h\|}_{\infty}}$ achieves value $1$? I think it's not possible.. | |
| Jun 5, 2020 at 14:22 | comment | added | Nik Weaver | By $\alpha$ do you mean $a$? Then yes, 1 is always a lower bound. | |
| Jun 5, 2020 at 14:18 | comment | added | ABIM | As a lower bound (when $\alpha \neq 0$) was always have 1, since the translation operator is hypercyclic no? | |
| Jun 5, 2020 at 13:58 | vote | accept | ABIM | ||
| Jun 5, 2020 at 13:56 | vote | accept | ABIM | ||
| Jun 5, 2020 at 13:56 | |||||
| Jun 5, 2020 at 13:47 | history | answered | Nik Weaver | CC BY-SA 4.0 |