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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Free analysis questions II: The Grassmannian completion and the series expansions at the origin

Dan-Virgil Voiculescu1

1Department of Mathematics, University of California at Berkeley, Berkeley CA 94720-3840, USA. e-mail:

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2010, Issue 645, Pages 155–236, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle.2010.063, August 2010

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The fully matricial generalization in part I, of the difference quotient derivation on holomorphic functions, in which ℂ is replaced by a Banach algebra B, is extended from the affine case to a Grassmannian completion. The infinitesimal bialgebra duality, the duality transform generalizing the Stieltjes transform and the spectral theory with non-commuting scalars all extend to this completion. The series expansions of fully matricial analytic functions are characterized, providing a new way to generate fully matricial functions.

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