Moshe Arens (1925–2019)

ABSTRACT COMPETENT PROGRAM EVOLUTION by Moshe Looks

Non Commutative Arens Algebras and Their Derivations

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...

Text difficulty and the Arens-Altmann law

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...

On the Arens Products and Certain Banach Algebras

In this paper, we study several problems in Banach algebras concerned with the Arens products.

Quasi-Multipliers on Weak Arens Regular Banach Algebras

In this paper we define the notion of weak Arens regular Banach algebras and extend the concept of quasi-multipliers to this certain class of Banach algebras. Among other the relationship between Arens regularity of the algebra A∗∗ of a weak Arens regular Banach algebra A and the space QMr(A∗) of all bilinear and separately continuous right quasimultipliers of A∗ is investigated. Further, we st...