Lebesgue decomposition of functionals and unique preduals for commutants modulo normed ideals
Operator Algebras
2016-08-26 v1 Functional Analysis
Abstract
We prove an analogue of the Lebesgue decomposition for continuous functionals on the commutant modulo a reflexive normed ideal of an n-tuple of hermitian operators for which there are quasicentral approximate units relative to the normed ideal. Using results of Godefroy-Talagrand and Pfitzner we derive from this strong uniqueness of the predual of such a commutant modulo a normed ideal.
Keywords
Cite
@article{arxiv.1608.07228,
title = {Lebesgue decomposition of functionals and unique preduals for commutants modulo normed ideals},
author = {Dan-Virgil Voiculescu},
journal= {arXiv preprint arXiv:1608.07228},
year = {2016}
}
Comments
12 pages preliminary version