On Invertible m-isometrical Extension of an m-isometry
Tóm tắt
We give necessary and sufficient conditions on an m-isometry to have an invertible m-isometrical extension. As particular cases, we give a useful characterization for a general m-isometrical unilateral weighted shift and for
$$\ell $$
-Jordan isometries. In particular, every
$$\ell $$
-Jordan isometry operator has an invertible
$$(2\ell -1)$$
-isometrical extension.
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