*-Doubles and embedding of associative algebras in $\\mathbf{B}(\\mathcal{H})$

Author:

Popovych   Stanislav  

Journal:

Indiana University Mathematics Journal

Issue Date:

2008

Abstract(summary):

We prove that an associative algebra Ais isomorphic to a subalgebra of aC*-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 Bwith the greatest C*-subalgebra consisting of the multiples of the unit and such that ...

Page:

3443-3462