Thank you!
i want apply this result $T^{*}(Pr_{C}(y)) = Pr_{T^{*}(C)}(T^{*}y)$, to
$Pr_{x + C}(y) = Pr_{C}(x + y)$ and $Pr_{\lambda C}(\lambda y) = \lambda Pr_{C}(y)$
by creating $T$ first and later deducing $T^{*}$ (i don't know if this is possible!),
i imagine maybe, just by letting $Ty...
Hello,
I want to show $ T^{*}(Pr_{C}(y)) = Pr_{T^{*}(C)}(T^{*}y)$
where $T \in B(H)$ and $TT^{*}=I$ , $H$ is Hilbert space and $C$ is a closed convex non empty set.
but i don't know how to start, or what tricks needed to solve this type of problems.
also i want know how to construct $T$ to...