Noncommutative Bennett and Rosenthal inequalities
نویسندگان
چکیده
منابع مشابه
Rosenthal Inequalities in Noncommutative Symmetric Spaces
We give a direct proof of the ‘upper’ Khintchine inequality for a noncommutative symmetric (quasi-)Banach function space with nontrivial upper Boyd index. This settles an open question of C. Le Merdy and the fourth named author [24]. We apply this result to derive a version of Rosenthal’s theorem for sums of independent random variables in a noncommutative symmetric space. As a result we obtain...
متن کاملNoncommutative Burkholder/Rosenthal inequalities II: applications
We show norm estimates for the sum of independent random variables in noncommutative Lp-spaces for 1 < p <∞ following our previous work. These estimates generalize the classical Rosenthal inequality in the commutative case. Among applications, we derive an equivalence for the p-norm of the singular values of a random matrix with independent entries, and characterize those symmetric subspaces an...
متن کاملOn the Khintchine and Rosenthal Inequalities in Noncommutative Symmetric Spaces
Probabilistic inequalities for independent random variables and martingales play a prominent role in many different areas of mathematical research, such as harmonic analysis, probability theory, Banach space geometry and the study of symmetric function spaces. In the recent years, many of these classical probabilistic inequalities have been generalized to the context of noncommutative Lp-spaces...
متن کاملRosenthal Type Inequalities for Free Chaos
Let A denote the reduced amalgamated free product of a family A1,A2, . . . , An of von Neumann algebras over a von Neumann subalgebra B with respect to normal faithful conditional expectations Ek : Ak → B. We investigate the norm in Lp(A) of homogeneous polynomials of a given degree d. We first generalize Voiculescu’s inequality to arbitrary degree d ≥ 1 and indices 1 ≤ p ≤ ∞. This can be regar...
متن کاملPseudo-localization of Singular Integrals and Noncommutative Littlewood-paley Inequalities
Understood in a wide sense, square functions play a central role in classical Littlewood-Paley theory. This entails for instance dyadic type decompositions of Fourier series, Stein’s theory for symmetric diffusion semigroups or Burkholder’s martingale square function. All these topics provide a deep technique when dealing with quasi-orthogonalitymethods, sums of independent variables, Fourier m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2013
ISSN: 0091-1798
DOI: 10.1214/12-aop771