The SOT-closure of the set of 2-isometries

2025/09/05 by Marcel Scherer, Scherer, Marcel
Decision Sciences · Mathematics · #47A05 (Primary) #47A20 (Secondary) #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.2509.05083

openalex publication_date 2025/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Bishop-like theorems for non-subnormal operators

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