let r be a prime ring with extended centroid c, h a generalized derivation of r and n ⩾ 1 a xed integer. in this paper we study the situations: (1) if (h(xy))n = (h(x))n(h(y))n for all x; y 2 r; (2) obtain some related result in case r is a noncommutative banach algebra and h is continuous or spectrally bounded.

We show that most of the theory of Hermitian Banach algebras can be proved for normed ∗-algebras without the assumption of completeness. The condition r(x) ≤ p(x) for all x (where p(x) = r(x∗x)1/2 is the Pták function), which is essential in the theory of Hermitian Banach algebras, is replaced for normed ∗-algebras by the condition r(x + y) ≤ p(x) + p(y) for all x, y. In case of Banach ∗-algebr...

We show that if T is an isometry (as metric spaces) between the invertible groups of unital Banach algebras, then T is extended to a surjective real-linear isometry up to translation between the two Banach algebras. Furthermore if the underling algebras are closed unital standard operator algebras, (T (eA)) −1 T is extended to a surjective real algebra isomorphism; if T is a surjective isometry...

let $a$ be an arbitrary banach algebra and $varphi$ a homomorphism from $a$ onto $bbb c$. our first purpose in this paper is to give some equivalent conditions under which guarantees a $varphi$-mean of norm one. then we find some conditions under which there exists a $varphi$-mean in the weak$^*$ cluster of ${ain a; |a|=varphi(a)=1}$ in $a^{**}$.

in this paper we investigate some hereditary properties of amenability modulo an ideal of banach algebras. we show that if (e) is a bounded approximate identity modulo i of a banach algebra a and x is a neo-unital modulo i, then (e) is a bounded approximate identity for x. moreover we show that amenability modulo an ideal of a banach algebra a can be only considered by the neo-unital modulo...

In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...

Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule with the left and right module actions $pi_ell: Atimes Xrightarrow X$ and $pi_r: Xtimes Arightarrow X$, respectively. In this paper, we  study  the topological centers of the left module action $pi_{ell_n}: Atimes X^{(n)}rightarrow X^{(n)}$ and the right module action $pi_{r_n}:X^{(n)}times Arightarrow X^{(n)}$,  which inherit from th...

In the paper we prove an extension theorem for matrices with entries in H (U) for U being a Riemann surface of a special type. One of the main components of the proof is a Grauert type theorem for “holomorphic” vector bundles defined over maximal ideal spaces of certain Banach algebras.