# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Studia Mathematica

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## Order theory and interpolation in operator algebras

### Tom 225 / 2014

Studia Mathematica 225 (2014), 61-95 MSC: Primary 46B40, 46L52, 46L85, 47L07, 47L30; Secondary 32T40, 46H10, 46L05, 46L07, 46L30. DOI: 10.4064/sm225-1-4

#### Streszczenie

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.

#### Autorzy

• David P. BlecherDepartment of Mathematics
University of Houston
Houston, TX 77204-3008, U.S.A.
e-mail
• Charles John ReadDepartment of Pure Mathematics
University of Leeds
Leeds LS2 9JT, England
e-mail

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