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- H. G. Dales
- 2006

In this paper, we define multi-normed spaces, and investigate some properties of multi-bounded mappings on multi-normed spaces. Moreover, we prove a generalized Hyers– Ulam–Rassias stability theorem associated to the Cauchy additive equation for mappings from linear spaces into multi-normed spaces.

- H. G. Dales, T. Lau
- 2007

Let A be a Banach algebra, with second dual space A′′. We propose to study the space A′′ as a Banach algebra. There are two Banach algebra products on A′′, denoted by 2 and 3 . The Banach algebra A is Arens regular if the two products 2 and 3 coincide on A′′. In fact, A′′ has two topological centres denoted by Z (1) t (A ′′) and Z (2) t (A ′′) with A ⊂ Z t… (More)

Let A be a Banach algebra, and let D :A −→ A∗ be a continuous derivation, where A∗ is the topological dual space of A. The paper discusses the situation when the second transpose D∗∗ :A∗∗ −→ (A∗∗)∗ is also a derivation in the case where A∗∗ has the first Arens product.

- H. G. Dales, R. J. Loy, Y. Zhang, Y. Zhang
- 2007

We consider when certain Banach sequence algebras A on the set N are approximately amenable. Some general results are obtained, and we resolve the special cases where A = ` p for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras ` (ω).

- H. G. Dales, Dona Strauss
- 2007

Let S be a semigroup, and let ` (S) be the Banach algebra which is the semigroup algebra of S. We shall study the structure of this Banach algebra and of its second dual. We shall determine exactly when ` (S) is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are ‘forbidden values’ for this constant. The second… (More)

- H. G. Dales
- 1998

- H. G. Dales
- 2007

Let G be a locally compact abelian group, and let p 2 1; 1). We show that the Segal algebra S p (G) is always weakly amenable, but that it is amenable only if G is discrete.

In [9], Dawson and the second author asked whether or not a Banach function algebra with dense invertible group can have a proper Shilov boundary. We give an example of a uniform algebra showing that this can happen, and investigate the properties of such algebras. We make some remarks on the topological stable rank of commutative, unital Banach algebras.… (More)

- H. G. Dales
- 2007

for each f, g ∈ L (G). For the theory of this Banach algebra, see [8], [14], [17], and [2, §3.3], for example. There are many standard left (and right) Banach L(G)-modules. Here we determine when these modules have certain well-known homological properties; we shall summarize some known results, and establish various new ones. In fact, we are seeking to… (More)

- H. G. Dales, Dona Strauss
- 2008

Let S be a (discrete) semigroup, and let ` (S) be the Banach algebra which is the semigroup algebra of S. We shall study the structure of this Banach algebra and of its second dual. We shall determine exactly when ` (S) is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are ‘forbidden values’ for this constant.… (More)