Let  $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $|aa_alpha-varphi(a)a_alpha|to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such  as Segal algebras and $L^1$-algebras are resp...

Let $ (A,| cdot |) $ be a real Banach algebra, a complex algebra $ A_mathbb{C} $ be a complexification of $ A $ and $ | | cdot | | $ be an algebra norm on  $ A_mathbb{C}  $  satisfying a simple condition together with the norm $ | cdot | $ on $ A$.  In this paper we first show that $ A^* $ is a real Banach $ A^{**}$-module if and only if $ (A_mathbb{C})^* $ is a complex Banach $ (A_mathbb{C})^{...

let $mathcal{r}$ be a  commutative ring with identity, let $a$ and $b$ be two $mathcal{r}$-algebras and $varphi:blongrightarrow a$ be an $mathcal{r}$-additive algebra homomorphism. we introduce a new algebra $atimes_varphi b$, and give some basic properties of this algebra. generalized $2$-cocycle derivations on $atimes_varphi b$ are studied. accordingly, $atimes_varphi b$ is considered from th...

We investigate the higher-dimensional amenability of tensor products A ⊗̂ B of Banach algebras A and B. We prove that the weak bidimension dbw of the tensor product A⊗̂B of Banach algebras A and B with bounded approximate identities satisfies dbwA ⊗̂ B = dbwA+ dbwB. We show that it cannot be extended to arbitrary Banach algebras. For example, for a biflat Banach algebra A which has a left or right...

In this paper, we investigate homomorphisms from unital C∗−algebras to unital Banach algebras and derivations from unital C∗−algebras to Banach A−modules related to a Cauchy–Jensen functional inequality. Mathematics subject classification (2010): 39B72, 46H30, 46B06.

We consider weakly coupled analytic expanding circle maps on the lattice Z d (for d 1), with small coupling strength and coupling between two sites decaying exponentially with the distance. We study the spectrum of the associated (Perron-Frobenius) transfer operators. We give a Fr echet space on which the operator associated to the full system has a simple eigenvalue at 1 (corresponding to the ...

Let  be a Banach algebra. Let  be linear mappings on . First we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple Banach algebras, in certain case. Afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

We give a two-line proof of long-standing conjecture Ben-Akiva and Lerman (1985) regarding the random utility representation nested logit model, thus providing renewed straightforward textbook treatment that model. As an application, we provide closed-form formula for correlation between two Fr\'echet variables coupled by Gumbel copula.

In a recent paper 10], Gowda and Ravindran introduced the concepts of H-diierentiability and H-diierential for a function f : R n ! R n and showed that the Fr echet derivative of a Fr echet diierentiable function, the Clarke generalized Jacobian of a locally Lips-chitzian function, the Bouligand subdiierential of a semismooth function, and the C-diierential of a C-diierentiable function are par...

‎in this paper‎, ‎using fixed point method‎, ‎we prove the generalized hyers-ulam stability of‎ ‎random homomorphisms in random $c^*$-algebras and random lie $c^*$-algebras‎ ‎and of derivations on non-archimedean random c$^*$-algebras and non-archimedean random lie c$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...