Learn More
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 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 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)
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)