2 00 9 ∗ - Doubles and embedding of associative algebras in B ( H ) .
نویسنده
چکیده
We prove that an associative algebra A is isomorphic to a subalgebra of a C∗-algebra if and only if its ∗-double A∗A∗ is ∗-isomorphic to a ∗-subalgebra of a C∗-algebra. In particular each operator algebra is shown to be completely boundedly isomorphic to an operator algebra B with the greatest C∗-subalgebra consisting of the multiples of the unit and such that each element in B is determined by its module up to a scalar multiple. We also study the maximal subalgebras of an operator algebra A which are mapped into C∗-algebras under completely bounded faithful representations of A.
منابع مشابه
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