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<p>We study <i>n</i>-isometric elementary operators of length one, highlighting the special case <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n=1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, which is fundamental due to the importance and practical relevance of classical isometries. In this case, we provide two proofs: one based on norm arguments and the other using an identification with tensor products and standard factorization properties. For arbitrary <i>n</i>, we furnish a direct proof of a result by Caixing Gu on <i>n</i>-isometric elementary operators of length one, relying solely on an antiunitary cosimilarity and a single lemma, and thereby eschewing the auxiliary arguments of the original work.</p>

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When is the elementary operator of length one an n-isometry?

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Mohamed Amine Aouichaoui

摘要

We study n-isometric elementary operators of length one, highlighting the special case \(n=1\) n = 1 , which is fundamental due to the importance and practical relevance of classical isometries. In this case, we provide two proofs: one based on norm arguments and the other using an identification with tensor products and standard factorization properties. For arbitrary n, we furnish a direct proof of a result by Caixing Gu on n-isometric elementary operators of length one, relying solely on an antiunitary cosimilarity and a single lemma, and thereby eschewing the auxiliary arguments of the original work.