Vol. 37(51), pp. 9399 (1985) 

Bases from orthogonal subspaces obtained by evaluation of the reproducing kernelDu\v san Georgijevi\'cMa\v sinski fakultet, Beograd, YugoslaviaAbstract: Every inner operator function $\theta$ with values in $B(E,E)$, $E$  a fixed (separable) Hilbert space, determines a coinvariant subspace $H(\theta)$ of the operator of multiplication by $z$ in the Hardy space $H^2_E$. ``Evaluating'' the reproducing kernel of $\,H(\theta)$ at ``Upoints'' of the function $\theta$ ($U$ is unitary operator) we obtain operator functions $\gamma_t(2)$ and subspaces $\gamma_tE$. The main result of the paper is: Let the operator $I\theta(z)U^*$ have a bounded inverse for every $z$ z<1$. If $(1r)^{1}\Re\varphi(rt)$ for definition of $\varphi$ see (1) is uniform bounded in $r$, $0\leq r<1$, for all $t$, t=1$, except for a countable set, then the familly of subspaces $\gamma_tE$ is orthogonal and complete in $H(\theta)$. This generalizes an analogous result of Clark [3] in the scalar case. Classification (MSC2000): 46E40 Full text of the article:
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
