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Harmonic Analysis of Operators on Hilbert Space
Contractions and Their Dilations.- Geometrical and Spectral Properties of Dilations.- Functional Calculus.- Extended Functional Calculus.- Operator-Valued Analytic Functions.- Functional Models.-Expand
STABLE LAWS AND DOMAINS OF ATTRACTION IN FREE PROBABILITY THEORY
In this paper we determine the distributional behavior of sums of free (in the sense of Voiculescu) identically distributed, inflnitesimal random variables. The theory is shown to parallel theExpand
A new approach to subordination results in free probability
We show that the subordination results of D. Voiculescu and Ph. Biane can be deduced from a continuity property of fixed points for analytic functions.
Operator Theory and Arithmetic in
An introduction to dilation theory The class $C_0$ Classification theory Applications of Jordan models Characteristic functions and the class $C_0$ Weak contractions Fredholm theory MiscellaneousExpand
Superconvergence to the central limit and failure of the Cramér theorem for free random variables
SummaryWe show that convergence of the semicircle law in the free central limit theorem for bounded random variables is much better than expected. Thus, the distributions which tend to the semicircleExpand
Dual Algebras with Applications to Invariant Subspaces and Dilation Theory
Dual algebras Simultaneous systems of equations in the predual of a dual algebra The properties $X_{\theta, \gamma}$ and the properties $(\mathbf A_n)$ Singly generated dual algebras Dilation theoryExpand
Lévy-Hinčin type theorems for multiplicative and additive free convolution.
We give a description of infinitely divisible compactly supported probability measures relative to the multiplicative free convolutions on the positive half-line and on the unit circle. A new proofExpand
HYPER-REFLEXIVITY AND THE FACTORIZATION OF LINEAR FUNCTIONALS
Abstract It is shown that hyper-reflexivity of a space of linear operators on a Hilbert space follows from a factorization property of linear functionals continuous in the weak operator topology.Expand
A spectral commutant lifting theorem
©1991 American Mathematical Society. First published in Transactions of the American Mathematical Society, Vol. 325, No. 2, June 1991 by the American Mathematical Society
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