Researchers have disproven a conjecture by Tang and Zhang regarding the Schatten norm, specifically the all-dimensional best constant in a matrix inequality. Using two explicit real 2x2 rank-one matrices at p=3/2, they demonstrated that the attained ratio exceeds 207/200, contradicting the conjectured constant. The paper also provides positive results, proving the conjectured sharp bound for rank-at-most-one summands when 2 <= p < infinity and classifying equality cases, along with the endpoint statement for p=infinity. Additionally, for arbitrary complex matrices, the conjectured sharp constant is established for m=2 and p=4. AI
RANK_REASON Academic paper published on arXiv presenting mathematical results. [lever_c_demoted from research: ic=1 ai=0.1]
AI-generated summary · Google Gemini · from 1 sources. How we write summaries →
