A hyponormal weighted shift on a directed tree whose square has trivial domain

Mathematics – Functional Analysis

Scientific paper

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8 pages

Scientific paper

It is proved that, up to isomorphism, there are only two directed trees that
admit a hyponormal weighted shift with nonzero weights whose square has trivial
domain. These are precisely those enumerable directed trees, one with root, the
other without, whose every vertex has enumerable set of successors.

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