We show that a non-expansive action of a topological semigroup S on a metric space X is linearizable iff its orbits are bounded. The crucial point here is to prove that X can be extended by adding a fixed point of S, thus allowing application of a semigroup version of the Arens-Eells linearization, iff the orbits of S in X are bounded.

For Φ,Ψ ∈ A′′, define 〈Φ Ψ, λ〉 = 〈Φ, Ψ · λ〉 (λ ∈ A′) , and similarly for ♦. Thus (A′′, ) and (A′′,♦) are Banach algebras each containingA as a closed subalgebra. The Banach algebra A is Arens regular if and ♦ coincide on A′′, and A is strongly Arens irregular if and ♦ coincide only on A. A subspace X of A′ is left-introverted if Φ · λ ∈ X whenever Φ ∈ A′′ and λ ∈ X . There has been a great deal...

A complex algebra A is called ideally factored if Ia = Ca is a left ideal of A for all a ∈ A. In this article, we investigate some interesting properties of ideally factored algebras and show that these algebras are always Arens regular but never amenable. In addition, we investigate ρhomomorphisms and (ρ, τ)-derivations on ideally factored algebra.

Let G be a locally compact non-compact group. We show that under a very mild assumption on the weight function w, the weighted group algebra L1(G, w) is strongly Arens irregular in the sense of [Dal–Lam–Lau 01]. To this end, we first derive a general factorization theorem for bounded families in the L∞ ( G, w ) ∗ -module L∞ ( G, w ) .

Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule with the left and right module actions $pi_ell: Atimes Xrightarrow X$ and $pi_r: Xtimes Arightarrow X$, respectively. In this paper, we  study  the topological centers of the left module action $pi_{ell_n}: Atimes X^{(n)}rightarrow X^{(n)}$ and the right module action $pi_{r_n}:X^{(n)}times Arightarrow X^{(n)}$,  which inherit from th...