Dual Banach algebras: Representations and injectivity

By Matthew Daws. 2006

61 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6e521544c38821c1c07b1e43e4d5ed3fc7eef3d4

How researchers see this paper

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In Algebra and Number Theory

1. Dona Strauss
2. Anthony To-Ming Lau
3. H. Garth Dales
4. Matthew Daws

In Mathematical Physics

1. Dona Strauss
2. Anthony To-Ming Lau
3. H. Garth Dales
4. Matthew Daws
5. M. S. Monfared

Citations in the corpus

• Multipliers, Self-Induced and Dual Banach Algebras (2010, background): “Following [47, 10], we say that a Banach algebra A which is the dual of a Banach space A∗ is a dual Banach algebra if multiplication in A is separately weak-continuous.”
• Banach Algebras on Semigroups and on Their Compactifications (2010, background): “For a recent account of dual Banach algebras, see [28].”