Let A be a Banach algebra, with second dual space Aâ€²â€². We propose to study the space Aâ€²â€² as a Banach algebra. There are two Banach algebra products on Aâ€²â€², denoted by 2 and 3 . The Banach algebra Aâ€¦ (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 Hyersâ€“ Ulamâ€“Rassias stability theoremâ€¦ (More)

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 shallâ€¦ (More)

for each f, g âˆˆ L (G). For the theory of this Banach algebra, see [8], [14], [17], and [2, Â§3.3], for example. There are many standard left (and right) Banach L(G)-modules. Here we determine whenâ€¦ (More)

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 â‰¤ p < âˆž, showingâ€¦ (More)

The conjecture that every algebra norm || â€¢ || on C(X) is equivalent to the uniform norm arises naturally from a theorem of Kaplansky in 1949 that necessarily 11/11 > \f\x ( Æ’ e C(X)): see [9, 10.1].â€¦ (More)

We address the following two questions regarding the maximal left ideals of the Banach algebra B(E) of bounded operators acting on an in nite-dimensional Banach space E : (I) Does B(E) always containâ€¦ (More)