Let and be mutually commuting unital C* subalgebras of (). It is shown that and are C* independent if and only if for all natural numbers n, m, for all n-tuples A = (A₁, ..., Aₙ) of doubly commuting nonzero operators of and m-tuples B = (B₁, ..., Bₘ) of doubly commuting nonzero operators of , , where Sp denotes the joint Taylor spectrum.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-3-1,
author = {Shuilin Jin and Li Xu and Qinghua Jiang and Li Li},
title = {Conditions equivalent to C* independence},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {191-197},
zbl = {1278.47015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-3-1}
}
Shuilin Jin; Li Xu; Qinghua Jiang; Li Li. Conditions equivalent to C* independence. Studia Mathematica, Tome 209 (2012) pp. 191-197. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-3-1/