Timeline for Why is this a conditional expectation into the fixed point algebra?
Current License: CC BY-SA 3.0
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| when toggle format | what | by | license | comment | |
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| Apr 25, 2011 at 13:44 | vote | accept | Steve | ||
| Apr 24, 2011 at 4:23 | comment | added | Dima Shlyakhtenko | Regarding the second question, if $x$ is an element in the $\ast$-algebra generated algebraically by the isometries, then $x$ is in the linear span of elements of the form $y=S_{i_1}\cdots S_{i_n} S_{j_1}^\ast \cdots S_{j_m}^\ast$. Since $\alpha_t(y)=\exp((n-m)t)y$, it follows from the formula for integration of trigonometric polynomials that $E(y)=0$ unless $n=m$ (in which case $E(y)=y$). | |
| Apr 23, 2011 at 12:32 | history | answered | Pieter Naaijkens | CC BY-SA 3.0 |