Let $R$ be a prime ring with extended centroid $C$, $H$ a generalized derivation of $R$ and $ngeq 1$ a fixed integer. In this paper we study the situations: (1) If $(H(xy))^n =(H(x))^n(H(y))^n$ for all $x,yin R$; (2) obtain some related result in case $R$ is a noncommutative Banach algebra and $H$ is continuous or spectrally bounded.

A Banach lattice algebra is a Banach lattice, an associative algebra with a sub-multiplicative norm and the product of positive elements should be positive. In this note we study the Arens regularity and cohomological properties of Banach lattice algebras.

In this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a Banach algebra $A$ into a semisimple Banach algebra $B$ is continuous.

We study Banach C̃-algebras, i.e., complete ultra-pseudo-normed algebras over the ring C̃ of Colombeau generalized complex numbers. We develop a spectral theory in such algebras. We show by explicit examples that important parts of classical Banach algebra theory do not hold for general Banach C̃algebras and indicate a particular class of Banach C̃-algebras that overcomes these limitations to a lar...

Let A be a Banach algebra. We study those closed ideals I of A for which the first cohomology group of A with coefficients in I is trivial; i.e. H(A, I) = {0}. We investigate such closed ideals when A is weakly amenable or biflat. Also we give some hereditary properties of ideal amenability.

We consider the problem of identifying the maximal ideals of a Banach algebra S that is contained in a larger Banach algebra B. If S is dense in B in an appropriate sense and if the spectral radii in S and B are the same, then S and B have the same maximal ideals. The result is illustrated by two examples of Banach algebras S in which the density and spectral radius conditions are easily shown ...

A Banach algebra A is weakly amenable provided that every bounded derivation from A to its dual A is inner. In H1], the rst-named author, building on earlier work of J. W. Bunce and W. L. Paschke BP], proved that every C-algebra is weakly amenable. We give a simpliied and uniied proof of this theorem. B. E. Johnson has proved that every bounded Jordan derivation from a C-algebra A to any Banach...

In this paper we prove that every n-Jordan homomorphis varphi:mathcal {A} longrightarrowmathcal {B} from unital Banach algebras mathcal {A} into varphi -commutative Banach algebra mathcal {B} satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0, xin mathcal {A}, is an n-homomorphism. In this paper we prove that every n-Jordan homomorphism varphi:mathcal {A} longrightarrowmathcal...