Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated 32 min ago
PreprintCC BY-NC-ND 4.0HAL

Optimal square size for separating the operator and completely bounded norms of Schur multipliers on S^4

  • Cédric Arhancet
Open at sourcePDFDOICite

Abstract

We determine the smallest square size at which the operator norm and the completely bounded norm of a Schur multiplier on S4 can differ. More precisely, for A=1&2&0 1&−2&0 2&2i&0 we prove |MA|S43→ S432≤1119/250 <(18983532/947485)1/2 ≤ |IdS42⊗ MA|S46→ S462. We also prove that no 2×2 Schur multiplier can have unequal operator and completely bounded norms on S4, so square size three is optimal. In addition, we determine the exact ordinary norm of the previous multiplier analytically and give an independent computer-assisted certification of a rational upper bound.

Related

  1. Schur Multipliers with Unequal Operator and Completely Bounded Norms on Sp, $1<p\ne 2<\infty $
    J. Huang, F. Sukochev, A. Tomskova
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. A Separable Hilbertian Operator Space with CBAP and No Completely Bounded Basis
    Dominique Guillot, Nicolas Cutrona
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  3. Bounded cohomology and optimal separating constant for representations
    Yushi Nakano, Teruhiko Soma
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  4. Optimal inequalities for completely bounded polynomials and the limitations of quantum query algorithms
    Francisco Escudero Gutiérrez, Miquel Saucedo, Carlos Palazuelos
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsQuantum physics & quantum informationarXiv
  5. Hadamard Rigidity and Sharp Stability in the Completely Bounded Bohnenblust--Hille Inequality
    Daniel Núñez-Alarcón, Daniel M. Pellegrino, Eduardo V. Teixeira
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{arhancet2026optimal,
  title = {{Optimal square size for separating the operator and completely bounded norms of Schur multipliers on S^4}},
  author = {Cédric Arhancet},
  howpublished = {HAL},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2609.29643},
  eprint = {2609.29643},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05739888v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Optimal square size for separating the operator and completely bounded norms of Schur multipliers on S^4
AU  - Cédric Arhancet
PY  - 2026
DA  - 2026/08/19
PB  - HAL
DO  - 10.48550/arxiv.2609.29643
UR  - https://hal.science/hal-05739888v1
AB  - We determine the smallest square size at which the operator norm and the completely bounded norm of a Schur multiplier on S^4 can differ. More precisely, for A=1&2&0 1&−2&0 2&2i&0 we prove |M_A|_S^4_3→ S^4_3^2≤1119/250 <(18983532/947485)^1/2 ≤ |Id_S^4_2⊗ M_A|_S^4_6→ S^4_6^2. We also prove that no 2×2 Schur multiplier can have unequal operator and completely bounded norms on S^4, so square size three is optimal. In addition, we determine the exact ordinary norm of the previous multiplier analytically and give an independent computer-assisted certification of a rational upper bound.
ER  -