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*-Doubles and Embedding of Associative Algebras in B (H)

Stanislav Popovych (Institutionen för matematiska vetenskaper)
Indiana University Mathematics Journal (0022-2518). Vol. 57 (2008), 7, p. 3443-3462.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: *-algebra, Hilbert space, operator algebra, C*-algebra, completely, bounded homomorphism, reducing ideal, embedding, C-STAR-ALGEBRAS, OPERATOR-ALGEBRAS, SIMILARITY PROBLEM, REPRESENTATIONS

Denna post skapades 2009-10-22.
CPL Pubid: 100527


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