Mathematics – Operator Algebras
Scientific paper
1997-10-17
Mathematics
Operator Algebras
47 pages, LaTeX2e
Scientific paper
The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital operator algebras. This allows to define invariant distances on the spectrum of commutative operator algebras analogous to the Caratheodory distance for complex manifolds. Moreover, unitizations of two-dimensional operator algebras with zero multiplication provide a rich class of counterexamples. Especially, several badly behaved quotients of function algebras are exhibited. Recently, Arveson has developed a model theory for d-contractions. Quotients of the operator algebra of the d-shift are much more well-behaved than quotients of function algebras. Completely isometric representations of these quotients are obtained explicitly. This provides a generalization of Nevanlinna-Pick theory. An important property of quotients of the d-shift algebra is that their quotients of finite dimension r have completely isometric representations by rxr-matrices. Finally, the class of commutative operator algebras with this property is investigated.
No associations
LandOfFree
Finite dimensional quotients of commutative 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 Finite dimensional quotients of commutative operator algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite dimensional quotients of commutative operator algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-83842