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Free Analysis Questions I: Duality Transform for the Coalgebra of $\partial_{X:B}$

Dan Voiculescu
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Abstract

A duality transform for the coalgebra of the free difference quotient derivation-multiplication of an operator with respect to a free algebra of scalars is constructed. The dual object is realized in an algebra of matricial analytic functions endowed with yet another generalization of the difference quotient derivation.

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Dan Voiculescu. 2003-06-10. Free Analysis Questions I: Duality Transform for the Coalgebra of $\partial_{X:B}$. https://arxiv.org/abs/math/0306172

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