Dual Banach algebras: representations and injectivity

• Autorzy: Matthew Daws
• Języki publikacji: EN

Abstrakty

EN

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.

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 178
• Numer: 3
• Strony: 231-275

Daty

wydano

2007

Twórcy

autor

Matthew Daws

• St. John's College, Oxford, OX1 3JP, UK

Identyfikatory

DOI

10.4064/sm178-3-3