let $mathcal{a}$ be a banach algebra with bai and $e$ be an introverted subspace of $mathcal{a'}$.in this paper we study the quotient arens regularity of $mathcal{a}$ with respect to $e$ and prove that the group algebra $l^1(g)$ for a locally compact group $g$, is quotient arens regular with respect to certain introverted subspace $e$ of $l^infty(g)$.some related result are given as well.

We first study some properties‎ ‎of $A$-module homomorphisms $theta:Xrightarrow Y$‎, ‎where $X$‎ ‎and $Y$ are Fréchet $A$-modules and $A$ is a unital‎ ‎Fréchet algebra‎. ‎Then we show that if there exists a‎ ‎continued bisection of the identity for $A$‎, ‎then $theta$ is‎ ‎automatically continuous under certain condition on $X$‎. ‎In‎ ‎particular‎, ‎every homomorphism from $A$ into certain‎ ‎Fr...

The present paper deals with the concept of left amenability for a wide range of Banach algebras known as Lau algebras. It gives a fixed point property characterizing left amenable Lau algebras in terms of left Banach -modules. It also offers an application of this result to some Lau algebras related to a locally compact group G, such as the Eymard-Fourier algebra A(G), the Fourier-Stieltjes al...

We develop results which show that elements in the radical of a commutative Banach algebra are often precluded from having prime-like properties if we avoid certain exceptional situations involving torsion elements. This makes the proof of the Singer-Wermer conjecture conceptually much clearer. It also motivates the de nition of an element having regular powers and allows us to strengthen our p...

This paper is concerned with partially defined derivations on Banach algebras and particularly on C*-algebras and H*-algebras, a subject whose study was motivated by the question of time evolution and spatial translation in quantum physics (see [2, 7] for a full account of the theory). It is well known [4] that everywhere defined derivations on semisimple Banach algebras are automatically conti...

A class of algebras is introduced that includes the unital Banach algebras over the complex numbers. Commutator results are proved for such algebras and used to establish spectral properties of certain elements of Banach algebras. 1. Introduction. In this note, we introduce a condition on an algebra motivated by the situation in which Schur's lemma [S1] is applicable. We say that algebras satis...