Schur bounded patterns and submajorisation
Edward McDonald, Fedor Sukochev, Dmitriy Zanin
TL;DR
This paper characterizes Schur bounded patterns of certain operator ideals, especially Schatten ideals with 0<p<1, and explores their relationship with submajorisation closure properties.
Contribution
It provides a characterization of Schur bounded patterns for ideals of compact operators, including non-closed Schatten ideals, and links these patterns to submajorisation closure.
Findings
Characterized Schur bounded patterns for Schatten ideals with 0<p<1.
Identified ideals not closed under submajorisation via their Schur bounded patterns.
Established a correspondence between Schur bounded patterns and submajorisation closure properties.
Abstract
We characterise the Schur bounded patterns of ideals of compact operators that are not closed under submajorisation, in particular the Schatten ideals with Conversely we characterise the ideals that are not closed under submajorisation by their Schur bounded patterns.
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