Difference between revisions of "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|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|unitary operator]] | + | for a certain [[Unitary operator|unitary operator]] $U\colon H_1\to H_2$ and all $x\in X$. Cf. [[Intertwining operator|Intertwining operator]]. |
Latest revision as of 16:52, 16 August 2014
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://encyclopediaofmath.org/index.php?title=Unitarily-equivalent_representations&oldid=18693
Unitarily-equivalent representations. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Unitarily-equivalent_representations&oldid=18693
This article was adapted from an original article by A.I. Shtern (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article