We show a polynomially boundend operator T is similar to a unitary operator if there is a singular unitary operator W and an injection X such that XT = WX. If, in addition, T is of class , then T itself is unitary.
@article{bwmeta1.element.bwnjournal-article-apmv66z1p11bwm,
author = {T. Ando and K. Takahashi},
title = {On operators with unitary r-dilations},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {11-14},
zbl = {0873.47004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p11bwm}
}
T. Ando; K. Takahashi. On operators with unitary ϱ-dilations. Annales Polonici Mathematici, Tome 66 (1997) pp. 11-14. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p11bwm/
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