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arXiv · 2006.15642

The Wold-type decomposition for $m$-isometries

Jakub Kośmider
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Abstract

The aim of this paper is to study the Wold-type decomposition in the class of $m$-isometries. One of our main results establishes an equivalent condition for an analytic $m$-isometry to admit the Wold-type decomposition for $m\ge2$. In particular, we introduce the $k$-kernel condition which we use to characterize analytic $m$-isometric operators which are unitarily equivalent to unilateral operator valued weighted shifts for $m\ge2$. As a result, we also show that $m$-isometric composition operators on directed graphs with one circuit containing only one element are not unitarily equivalent to unilateral weighted shifts. We also provide a characterization of $m$-isometric unilateral operator valued weighted shifts with positive and commuting weights.

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BibTeXRIS

Jakub Kośmider. 2020-06-28. The Wold-type decomposition for $m$-isometries. https://doi.org/10.1007/s40840-021-01129-4

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