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Abstract: We give criteria for products of Toeplitz and Hankel operators on the Fock (Segal-Bargmann) space to belong to the Dixmier class, and compute their Dixmier trace. At the same time, analogous...
A Fock Space Model for Addition and Multiplication of C-free Random Variables
free independence c-free independence creation/annihilation operators
2010/12/31
The paper presents a Fock space model suitable for constructions of c-free algebras. Immediate applications are direct proofs for the properties of the c-free R- and S-transforms.
Exactness of the Fock space representation of the q-commutation relations
Exactness Fock space representation q-commutation relations
2010/9/1
We show that for all q in the interval (−1, 1), the Fock repre-sentation of the q-commutation relations can be unitarily embedded into the Fock representation of the extended Cuntz algebra. In p...