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Rademacher Cotype

For q>=2, the Rademacher cotype-q constant C_q^r(U) of a bounded operator U:X->Y between Banach spaces is the least constant such that

(sum_(i)||Ux_i||^q)^(1/q)<=C_q^r(U)E||sum_(i)epsilon_ix_i||,

where the inequality holds for every finite sequence (x_i) in X and the epsilon_i are independent random variables taking the values -1 and 1 with equal probability. The operator U has Rademacher cotype q when C_q^r(U) is finite. The Rademacher cotype of a Banach space X is the Rademacher cotype of its identity operator.

See also

Gaussian Cotype, Operator Cotype

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References

Talagrand, M. Upper and Lower Bounds for Stochastic Processes: Decomposition Theorems, 2nd ed. Cham, Switzerland: Springer, 2021. https://doi.org/10.1007/978-3-030-82595-9.

Cite this as:

Weisstein, Eric W. "Rademacher Cotype." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RademacherCotype.html

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