Analytic function theory for operator-valued free probability
نویسندگان
چکیده
منابع مشابه
Free Deterministic Equivalents, Rectangular Random Matrix Models, and Operator-Valued Free Probability Theory
Motivated by the asymptotic collective behavior of random and deterministic matrices, we propose an approximation (called " free determin-istic equivalent ") to quite general random matrix models, by replacing the matrices with operators satisfying certain freeness relations. We comment on the relation between our free deterministic equivalent and deterministic equivalents considered in the eng...
متن کاملHardy space of operator-valued analytic functions
We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of C. In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not suitable. Several properties (the Garsia-norm equivalent theorem, Carleson measure, and so on) of BMOA spaces are extended to the operator-valued setting. Then, the operat...
متن کاملOperator Probability Theory
This article presents an overview of some topics in operator probability theory. We do not strive for generality and only simple methods are employed. To give the reader a flavor of the subject we concentrate on the two most important topics, the law of large numbers and the central limit theorem.
متن کاملA Boolean-valued probability theory
New foundations for probability theory are suggested and investigated, derived from the formalized systems theory and using also some other branches of mathematical logic. The probability measures are supposed to take their values not in the unit interval of reals, but in a special kind of Boolean algebras. Some analogies as well as differences of this approach with respect to the classical Kol...
متن کاملA Sharp Maximal Function Estimate for Vector-Valued Multilinear Singular Integral Operator
We establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. As an application, we obtain the $(L^p, L^q)$-norm inequality for vector-valued multilinear operators.
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: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2017
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle-2014-0106