Talagrand's operator cotype problem

For a bounded operator $U$ between Banach spaces, write $C_q^r(U)$ for its Rademacher cotype-$q$ constant, $C_q^g(U)$ for its Gaussian cotype-$q$ constant and $\|U\|_{q,1}$ for its $(q,1)$-summing norm. Talagrand asked, as a research problem in his book on upper and lower bounds for stochastic processes, whether there is a universal constant $L$ with $C_q^r(U) \le L\max\{C_q^g(U), \|U\|_{q,1}\}$ for every such $U$. Is the Rademacher cotype of an operator controlled in this way?

Result

Disproved(see note)

Status

Resolved

AI contribution

AI-discovered

Method

Construction

Field

Banach space theory; stochastic processes

Posed by

Michel Talagrand, Research Problem 19 in Upper and Lower Bounds for Stochastic Processes (2nd edition, 2021)

Year posed

2021

Years open

5y

Solved

2026-09-17

Model

ChatGPT (GPT-5.6)

Vendor

OpenAI

Collaborators

Xinglong Wu

Verification

Unreviewed

Publication

Preprint

Significance

32 / 100*

Disclosed cost

—

Wikipedia

No dedicated article