On the Interaction between a Group of Unitary Operators and a Projection

S. W. Taylor, W. Littman


We consider the following objects: ${cal S}$ is a closed subspace of a
Hilbert Space ${cal H}$, ${cal P}$ is the projection operator for ${cal
S}$, and ${cal U}(t)$ is a strongly continuous group of unitary operators on
${cal H}$ with infinitesimal generator ${cal A}$. We let $U={cal U}(T)$,
where $T>0$ is fixed. The questions that we ask are
item Under what conditions is $mathcal{P}Umathcal{P}$ a contraction?
item Under what conditions can we steer $g in mathcal{S}$ to $hin mathcal{S}$ in the sense that we can find $fin
mathcal{H}$ such that ${cal P}f=g$ and ${cal P}Uf=h$?

control, Hilbert space, over-determined

Math Review Classification
Primary 47A50, 93C20 ; Secondary 35N10, 35N05

Last Updated
17 May 1999

6 pages

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