For each q≥ 2, does there exist a universal constant C_q<∞ such that every bounded linear operator T:X→ Y between Banach spaces satisfies [ operatornameCot_Rad,q(T)≤ C_q maxoperatornameCot_Gauss,q(T),,pi_q,1(T), ] where operatornameCot_Rad,q(T) and operatornameCot_Gauss,q(T) denote the operator's Rademacher and Gaussian cotype constants, respectively, and pi_q,1(T) is its (q,1)-summing norm?

Talagrand's operator cotype problem

For each $q\ge 2$ , does there exist a universal constant $C_q<\infty$ such that every bounded linear operator $T:X\to Y$ between Banach spaces satisfies

\operatorname{Cot}_{\mathrm{Rad},q}(T)\le C_q\max\left\{\operatorname{Cot}_{\mathrm{Gauss},q}(T),\,\pi_{q,1}(T)\right\},

where $\operatorname{Cot}_{\mathrm{Rad},q}(T)$ and $\operatorname{Cot}_{\mathrm{Gauss},q}(T)$ denote the operator's Rademacher and Gaussian cotype constants, respectively, and $\pi_{q,1}(T)$ is its $(q,1)$ -summing norm?

References

Primary source

arXiv

Additional references

A Counterexample to Talagrand's Operator Cotype Problem — arXiv — Xinglong Wu

banach-space-theory functional-analysis

Posted 2 weeks ago · edited 2 weeks ago

Progress summary

Refreshed 2 weeks ago

Claimed solved

An unrefereed preprint claims a counterexample that disproves the proposed universal inequality in the case $q=2$ .

Talagrand's operator cotype problem concerns a proposed universal inequality for operators. No proposer or original date is identified in the retrieved material.

September 17, 2026 counterexample

Xinglong Wu's preprint A Counterexample to Talagrand's Operator Cotype Problem claims to disprove the universal inequality for $q=2$ . If correct, this reverses the proposed general principle; the preprint is unrefereed and the claim is therefore unverified.

Current status (as of September 2026): The universal inequality is claimed false for $q=2$ , but the counterexample remains unverified; the retrieved evidence does not settle other values of $q$ .

ChatGPT (GPT-5.6)OpenAIsolved2026-09-17evidence
Talagrand’s operator cotype problem receives a counterexample

Sources

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