*-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.

operator algebra

embedding

Hilbert space

SIMILARITY PROBLEM

C*-algebra

REPRESENTATIONS

C-STAR-ALGEBRAS

*-algebra

reducing ideal

OPERATOR-ALGEBRAS

completely

bounded homomorphism

Författare

Stanislav Popovych

Göteborgs universitet

Chalmers, Matematiska vetenskaper

Indiana University Mathematics Journal

0022-2518 (ISSN)

Vol. 57 7 3443-3462

Ämneskategorier

Matematik

DOI

10.1512/iumj.2008.57.3422