Tracial joint spectral measures

• 成果类型: Article
• 署名作者: Heinavaara, Otte
• 署名单位: Princeton University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01309-6
• 发表日期: 2025
• 页码: 505-526
• 关键词: INEQUALITIES

摘要

Given two Hermitian matrices, A and B, we introduce a new type of spectral measure, a tracial joint spectral measure mu A, B on the plane. Existence of this measure implies the following two results: 1) any two-dimensional subspace of the Schatten-p class is isometric to a subspace of Lp, and 2) if f : R R has non-negative kth derivative and A and B are Hermitian matrices with A positive semidefinite, then t trf (tA + B) has non-negative kth derivative. We also give an explicit expression for the measure mu A,B.