The case of equality in Young's inequality for the s-numbers in semi-finite von Neumann algebras

Gabriel Larotonda

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arXiv · 1706.07115

The case of equality in Young's inequality for the s-numbers in semi-finite von Neumann algebras

Gabriel Larotonda

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Abstract

For a semi-finite von Neumann algebra $\mathcal A$, we study the case of equality in Young's inequality of s-numbers for a pair of $\tau$-measurable operators $a,b$, and we prove that equality is only possible if $|a|^p=|b|^q$. We also extend the result to unbounded operators affiliated with $\mathcal A$, and relate this problem with other symmetric norm Young inequalities.

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BibTeX RIS

Gabriel Larotonda. 2017-06-21. The case of equality in Young's inequality for the s-numbers in semi-finite von Neumann algebras. https://arxiv.org/abs/1706.07115

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