Page 1

Displaying 1 – 4 of 4

Showing per page

Derivations into iterated duals of Banach algebras

H. Dales, F. Ghahramani, N. Grønbæek (1998)

Studia Mathematica

We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space A ( n ) is zero; i.e., 1 ( A , A ( n ) ) = 0 . Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable; we study...

Dual Banach algebras: representations and injectivity

Matthew Daws (2007)

Studia Mathematica

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....

Currently displaying 1 – 4 of 4

Page 1