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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.
Let G be a locally compact group. We shall study the Banach algebras which are the group algebra L 1 (G) and the measure algebra M (G) on G, concentrating on their second dual algebras. As a preliminary we shall study the second dual C0(Ω) of the C *-algebra C0(Ω) for a locally compact space Ω, recognizing this space as C(Ω), where Ω is the hyper-Stonean… (More)
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.
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 (j) t (A) ⊂ A (j =… (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.
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 p (ω).