Schur coupling and related equivalence relations for operators on a Hilbert space

2014/02/20 by Dan Timotin, Timotin, Dan
Mathematics · #15A99 #47A05 #47A64 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1402.5046

openalex publication_date 2014/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For operators on Hilbert spaces of any dimension, we show that equivalence after extension coincides with equivalence after one-sided extension, thus obtaining a proof of their coincidence with Schur coupling. We also provide a concrete description of this equivalence relation in several cases, in particular for compact operators.

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