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Unitarily-equivalent representations

From Encyclopedia of Mathematics
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Representations $\pi_1$, $\pi_2$ of a group (algebra, ring, semi-group, cf. Representation of a group) $X$ in Hilbert spaces $H_1$, $H_2$, satisfying the condition

$$U\pi_1(x)=\pi_2(x)U$$

for a certain unitary operator $U\colon H_1\to H_2$ and all $x\in X$. Cf. Intertwining operator.

How to Cite This Entry:
Unitarily-equivalent representations. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Unitarily-equivalent_representations&oldid=32970
This article was adapted from an original article by A.I. Shtern (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article