Recent content by mathzero

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...