*-Doubles and Embedding of Associative Algebras in B (H)
Artikel i vetenskaplig tidskrift, 2008
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 13 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.