*-Doubles and Embedding of Associative Algebras in B (H)
Journal article, 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.
operator algebra
embedding
Hilbert space
SIMILARITY PROBLEM
C*-algebra
REPRESENTATIONS
C-STAR-ALGEBRAS
*-algebra
reducing ideal
OPERATOR-ALGEBRAS
completely
bounded homomorphism
Author
Stanislav Popovych
University of Gothenburg
Chalmers, Mathematical Sciences
Indiana University Mathematics Journal
0022-2518 (ISSN)
Vol. 57 7 3443-3462Subject Categories
Mathematics
DOI
10.1512/iumj.2008.57.3422