English

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