Given a von Neumann algebra M with a faithful normal semi-finite trace τ, we consider the non commutative Arens algebra Lω(M, τ) = ⋂ p≥1 Lp(M, τ) and the related algebras L2 (M, τ) = ⋂ p≥2 Lp(M, τ) and M + L2 (M, τ) which are proved to be complete metrizable locally convex *-algebras. The main purpose of the present paper is to prove that any derivation of the algebra M + L2 (M, τ) is inner and...

The study of text difficulty is considered to be an important issue for many branches of applied research. In the fields of journalism or education, for example, it is particularly important to know if (or to what degree) a given text is likely to cause difficulties for a recipient, or a group of recipients, i.e., if it is likely to be on an adequate (intended) level of difficulty or beyond. In...

in this paper, we study the arens regularity properties of module actions and we extend some proposition from baker, dales, lau and others into general situations. we establish some relationships between the topological centers of module actions and factorization properties of them with some results in group algebras. in 1951 arens shows that the second dual of banach algebra endowed with the e...

In this paper we provide upper estimates for the global projective dimensions of smooth crossed products $$\mathscr {S}(G, A; \alpha )$$ $$G = \mathbb {R}$$ and {T}$$ a self-induced Fréchet–Arens–Michael algebra A. To do this, powerful generalization methods which are used in works Ogneva Helemskii.

We show that the Lipschitz structure of a separable quasi-Banach space does not determine, in general, its linear structure. Using the notion of the Arens-Eells p-space over a metric space for 0 < p ≤ 1 we construct examples of separable quasi-Banach spaces which are Lipschitz isomorphic but not linearly isomorphic.

in this paper, we  study the arens regularity properties of module actions. we investigate some properties of topological centers of module actions ${z}^ell_{b^{**}}(a^{**})$ and  ${z}^ell_{a^{**}}(b^{**})$ with some conclusions in group algebras.