Hereditary subalgebras of operator algebras

Details Hereditary subalgebras of operator algebras Hereditary subalgebras of operator algebras

2005-12-17

arxiv.org/abs/math/0512417v3

Mathematics

Operator Algebras

Final version, To appear. 21 pages

Scientific paper

In recent work of the second author, a technical result was proved establishing a bijective correspondence between certain open projections in a C*-algebra containing an operator algebra A, and certain one-sided ideals of A. Here we give several remarkable consequences of this result. These include a generalization of the theory of hereditary subalgebras of a C*-algebra, and the solution of a ten year old problem on the Morita equivalence of operator algebras. In particular, the latter gives a very clean generalization of the notion of Hilbert C*-modules to nonselfadjoint algebras. We show that an `ideal' of a general operator space X is the intersection of X with an `ideal' in any containing C*-algebra or C*-module. Finally, we discuss the noncommutative variant of the classical theory of `peak sets'.

Affiliated with

Also associated with

No associations

Rating

Hereditary subalgebras of operator algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hereditary subalgebras of operator algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hereditary subalgebras of operator algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-298682