Dual Banach algebras: representations and injectivity

Matthew Daws. "Dual Banach algebras: representations and injectivity." Studia Mathematica 178.3 (2007): 231-275. <http://eudml.org/doc/284599>.

@article{MatthewDaws2007,
abstract = {We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of GNS type arguments. We define a notion of injectivity for dual Banach algebras, and show that this is equivalent to Connes-amenability. We conclude by looking at the problem of defining a well-behaved tensor product for dual Banach algebras.},
author = {Matthew Daws},
journal = {Studia Mathematica},
keywords = {injectivity; representation on a reflexive Banach space; dual Banach algebra; von Neumann algebra; Connes amenability; group algebra; unique predual},
language = {eng},
number = {3},
pages = {231-275},
title = {Dual Banach algebras: representations and injectivity},
url = {http://eudml.org/doc/284599},
volume = {178},
year = {2007},
}

TY - JOUR
AU - Matthew Daws
TI - Dual Banach algebras: representations and injectivity
JO - Studia Mathematica
PY - 2007
VL - 178
IS - 3
SP - 231
EP - 275
AB - We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of GNS type arguments. We define a notion of injectivity for dual Banach algebras, and show that this is equivalent to Connes-amenability. We conclude by looking at the problem of defining a well-behaved tensor product for dual Banach algebras.
LA - eng
KW - injectivity; representation on a reflexive Banach space; dual Banach algebra; von Neumann algebra; Connes amenability; group algebra; unique predual
UR - http://eudml.org/doc/284599
ER -