Order theory and interpolation in operator algebras

David P. Blecher, and Charles John Read. "Order theory and interpolation in operator algebras." Studia Mathematica 225.1 (2014): 61-95. <http://eudml.org/doc/285731>.

@article{DavidP2014,
abstract = {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.},
author = {David P. Blecher, Charles John Read},
journal = {Studia Mathematica},
keywords = {nonselfadjoint algebras; ordered linear spaces; accretive operators; noncommutative Urysohn lemma; Tietze theorem},
language = {eng},
number = {1},
pages = {61-95},
title = {Order theory and interpolation in operator algebras},
url = {http://eudml.org/doc/285731},
volume = {225},
year = {2014},
}

TY - JOUR
AU - David P. Blecher
AU - Charles John Read
TI - Order theory and interpolation in operator algebras
JO - Studia Mathematica
PY - 2014
VL - 225
IS - 1
SP - 61
EP - 95
AB - 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.
LA - eng
KW - nonselfadjoint algebras; ordered linear spaces; accretive operators; noncommutative Urysohn lemma; Tietze theorem
UR - http://eudml.org/doc/285731
ER -