An operator triangle inequality for the quadratic symmetric modulus
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918450320900096 |
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| author | Zhang, Teng |
| author_facet | Zhang, Teng |
| contents | 50 years after Thompson's famous triangle inequality for the operator right modulus, we establish a triangle inequality for the quadratic symmetric modulus. We also discuss the corresponding equality cases as well as the infinite-dimensional setting. In addition, we obtain Clarkson--McCarthy type inequalities for the quadratic symmetric modulus. Moreover, we answer several questions raised by Bourin and Lee in [\emph{Bull. Lond. Math. Soc.} \textbf{44} (2012), no.~6, 1085--1102] and [\emph{Internat. J. Math.} \textbf{31} (2026), no.~6, 2650018]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01463 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An operator triangle inequality for the quadratic symmetric modulus Zhang, Teng Functional Analysis Primary 47A63, Secondary 47A30, 47A05 50 years after Thompson's famous triangle inequality for the operator right modulus, we establish a triangle inequality for the quadratic symmetric modulus. We also discuss the corresponding equality cases as well as the infinite-dimensional setting. In addition, we obtain Clarkson--McCarthy type inequalities for the quadratic symmetric modulus. Moreover, we answer several questions raised by Bourin and Lee in [\emph{Bull. Lond. Math. Soc.} \textbf{44} (2012), no.~6, 1085--1102] and [\emph{Internat. J. Math.} \textbf{31} (2026), no.~6, 2650018]. |
| title | An operator triangle inequality for the quadratic symmetric modulus |
| topic | Functional Analysis Primary 47A63, Secondary 47A30, 47A05 |
| url | https://arxiv.org/abs/2602.01463 |