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arXiv · 2509.05083

The SOT-closure of the set of 2-isometries

Marcel Scherer
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Abstract

We show that the set of $2$-isometries on an infinite-dimensional Hilbert space is not closed in the strong operator topology. In fact, we prove that its SOT-closure coincides with the set of all expansive operators.

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Marcel Scherer. 2025-09-05. The SOT-closure of the set of 2-isometries. https://arxiv.org/abs/2509.05083

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