#
nLab

relative commutant

# Contents

## Definition

Let $\mathcal{A} \subset \mathcal{B}$ be an inclusion of $*-$ algebras. The *relative commutant* $\mathcal{A}^c(\mathcal{B})$ is defined by

$\mathcal{A}^c(\mathcal{B}) := \{ B \in \mathcal{B} : B A = A B, \; A \in \mathcal{A} \}$

If the algebras are operator algebras defined on a Hilbert space, then

$\mathcal{A}^c(\mathcal{B}) = \mathcal{A}' \bigcap \mathcal{B}$

Last revised on May 4, 2011 at 09:37:36.
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