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- Iushchenko, Kateryna, 1984, et al.
(författare)
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Matrix Ordered Operator Algebras
- 2007
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Ingår i: Indiana University Journ. Math..
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Annan publikation (övrigt vetenskapligt/konstnärligt)
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- Juschenko, Kate, 1984
(författare)
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Ideals of a C*-algebra generated by an operator algebra
- 2010
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 266:3, s. 693-705
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider ideals of a C*-algebra C*(B) generated by an operator algebra B. A closed ideal J subset of C*(B) is called a K-boundary ideal if the restriction of the quotient map on B has a completely bounded inverse with cb-norm equal to K-1. For K = 1 one gets the notion of boundary ideals introduced by Arveson. We study properties of the K-boundary ideals and characterize them in the case when operator algebra lambda-norms itself. Several reformulations of the Kadison similarity problem are given. In particular, the affirmative answer to this problem is equivalent to the statement that every bounded homomorphism from C*( B) onto B which is a projection on B is completely bounded. Moreover, we prove that Kadison's similarity problem is decided on one particular C*-algebra which is a completion of the *-double of M-2(C).
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| 9. |
- Juschenko, Kate, 1984, et al.
(författare)
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Matrix Ordered Operator Algebras
- 2009
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Ingår i: Indiana University Mathematics Journal. - : Indiana University Mathematics Journal. - 0022-2518. ; 58:3, s. 1203-1218
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Tidskriftsartikel (refereegranskat)abstract
- We study the question when for a given *-algebra,A a sequence of cones C-n subset of M-n (A)(sa) can be realized as cones of positive operators in a faithful *-representation of A on a Hilbert space. We present a criterion analogous to Effros-Choi abstract characterization of operator systems. A characterization of operator algebras which are completely boundedly isomorphic to C*-algebras is also presented.
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