Closedness of the orbit-closed C-numerical range and submajorization

2021/06/21 by Jireh Loreaux, Loreaux, Jireh, Sasmita Patnaik +1
Mathematics · #26D15 (Secondary) #47A12 #47B15 (Primary) 52A10 #52A40 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2106.11205

openalex publication_date 2021/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a positive trace-class operator C and a bounded operator A, we provide an explicit description of the closure of the orbit-closed C-numerical range of A in terms of those operators submajorized by C and the essential numerical range of A. This generalizes and subsumes recent work of Chan, Li and Poon for the k-numerical range, as well as some of our own previous work on the orbit-closed C-numerical range.

Citations

• The joint k-numerical range of operators

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