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- W4302418027 abstract "Let $S$ be a subspace of $L^2 (bm{R})$. We show that the operator $M$ of multiplication by the independent variable has a simple symmetric regular restriction to $S$ with deficiency indices $(1,1)$ if and only if $S = u h K^{2}_theta$ is a nearly invariant subspace, with $theta$ a meromorphic inner function vanishing at $i$. Here $u$ is unimodular, $h$ is an isometric multiplier of $K^{2}_theta$ into $H^2$ and $H^2$ is the Hardy space of the upper half plane. Our proof uses the dilation theory of completely positive maps." @default.
- W4302418027 created "2022-10-06" @default.
- W4302418027 creator A5073323884 @default.
- W4302418027 date "2012-07-12" @default.
- W4302418027 modified "2023-09-28" @default.
- W4302418027 title "Near invariance and symmetric operators" @default.
- W4302418027 doi "https://doi.org/10.48550/arxiv.1207.2931" @default.
- W4302418027 hasPublicationYear "2012" @default.
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