Injective and projective Hilbert C*-modules, and C*-algebras of compact operators

Details Injective and projective Hilbert C*-modules, and C*-algebras of compact operators Injective and projective Hilbert C*-modules, and C*-algebras of compact operators

2006-11-12

arxiv.org/abs/math/0611349v2

Mathematics

Operator Algebras

28 pages, Proposition 3.4 corrected after receiving remarks from Hanfeng Li, thanks for pointing out the errors. Some minor co

Scientific paper

We consider projectivity and injectivity of Hilbert C*-modules in the categories of Hilbert C*-(bi-)modules over a fixed C*-algebra of coefficients (and another fixed C*-algebra represented as bounded module operators) and bounded (bi-)module morphisms, either necessarily adjointable or arbitrary ones. As a consequence of these investigations, we obtain a set of equivalent conditions characterizing C*-subalgebras of C*-algebras of compact operators on Hilbert spaces in terms of general properties of Hilbert C*-modules over them. Our results complement results recently obtained by B. Magajna, J. Schweizer and M. Kusuda. In particular, all Hilbert C*-(bi-)modules over C*-algebras of compact operators on Hilbert spaces are both injective and projective in the categories we consider. For more general C*-algebras we obtain classes of injective and projective Hilbert C*-(bi-)modules.

Affiliated with

Also associated with

No associations

Rating

Injective and projective Hilbert C*-modules, and C*-algebras of compact operators 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 Injective and projective Hilbert C*-modules, and C*-algebras of compact operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Injective and projective Hilbert C*-modules, and C*-algebras of compact operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-729670