# Subrepresentation of a representation

From Encyclopedia of Mathematics

A linear representation $ \rho $
in an invariant subspace $ F \subset E $
of a representation $ \pi $
of a group (algebra, ring or semi-group) $ X $
in a (topological) vector space $ E $
defined by the formula $ \rho ( x) \xi = \pi ( x) \xi $
for all $ \xi \in F $,
$ x \in X $.
If $ \pi $
is a continuous representation (of a topological group, algebra, ring, or semi-group), then any subrepresentation of it is also continuous.

**How to Cite This Entry:**

Subrepresentation of a representation.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Subrepresentation_of_a_representation&oldid=48900

This article was adapted from an original article by A.I. Shtern (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article