Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
- 46A25: Reflexivity and semi-reflexivity
- 47L10: Algebras of operators on Banach spaces and other topological linear spaces
- 46A35: Summability and bases
- 46H99: None of the above, but in this section
- 46M05: Tensor products
- 46A32: Spaces of linear operators; topological tensor products; approximation properties
- 46H05: General theory of topological algebras
- 46L10: General theory of von Neumann algebras
- 43A20: L 1 -algebras on groups, semigroups, etc.
- 43A10: Measure algebras on groups, semigroups, etc.
- 46L06: Tensor products of C * -algebras
- 46H15: Representations of topological algebras
- 46B70: Interpolation between normed linear spaces
- 46M10: Projective and injective objects
Czasopismo
Rocznik
Tom
Numer
Strony
231-275
Opis fizyczny
Daty
wydano
2007
Twórcy
autor
- St. John's College, Oxford, OX1 3JP, UK
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-3-3