Order theory and interpolation in operator algebras

• Autorzy: David P. Blecher , Charles John Read
• Języki publikacji: EN

Abstrakty

EN

In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. Here we continue to develop this positivity and its associated ordering, proving many foundational facts. We also give many applications, for example to noncommutative topology, noncommutative peak sets, lifting problems, peak interpolation, approximate identities, and to order relations between an operator algebra and the C*-algebra it generates. In much of this it is not necessary that the algebra have an approximate identity. Many of our results apply immediately to function algebras, but we will not take the time to point these out, although most of these applications seem new.

Kategorie tematyczne

• 46L05: General theory of C * -algebras
• 46H10: Ideals and subalgebras
• 47L30: Abstract operator algebras on Hilbert spaces
• 46L52: Noncommutative function spaces
• 46L07: Operator spaces and completely bounded maps
• 46L85: Noncommutative topology
• 32T40: Peak functions
• 47L07: Convex sets and cones of operators
• 46L30: States
• 46B40: Ordered normed spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 225
• Numer: 1
• Strony: 61-95

Daty

wydano

2014

Twórcy

autor

David P. Blecher

• Department of Mathematics, University of Houston, Houston, TX 77204-3008, U.S.A.

autor

Charles John Read

• Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England

Identyfikatory

DOI

10.4064/sm225-1-4