Given two contractions T and T' such that T'-T is an operator of finite rank, we prove, under some conditions, the unitary equivalence of the unitary parts of the minimal isometric dilations (respectively minimal co-isometric extensions) of T and T'.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-3-4, author = {Chafiq Benhida}, title = {Unitary equivalence of operators and dilations}, journal = {Studia Mathematica}, volume = {162}, year = {2004}, pages = {253-255}, zbl = {1066.47006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-3-4} }
Chafiq Benhida. Unitary equivalence of operators and dilations. Studia Mathematica, Tome 162 (2004) pp. 253-255. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-3-4/